The main speedlight features to consider are:
Speedlights (hotshoe flashes; distinct from outlet-powered studio strobes which are also flashes) are powered by AA batteries. As strobes go, they're the low end of the totem pole when it comes to power, so every spare bit of it you can scrape together is useful. The power output of a flash is generally given as its guide number. The guide number, when divided by the f-number of the aperture setting, gives you the distance the light will travel at iso 100. But a lot of companies can cheat this by setting the flash to its highest zoom rating (more below) to make the number look higher. If you're going to be comparing apples to apples, make sure the zoom setting is the same across the flashes, or look at a review where the power output was actually measured with a light meter (e.g., this one on speedlights.net).
The higher the power output, the bigger and more expensive the flash will be, but the more useful it becomes. Think of the power output as you would the maximum aperture on a lens.
Tilt and swivel allow you to position the head of the flash in a different orientation to the body. This becomes important for two reasons. When you use a flash on-camera, the go-to method for diffusing the light and making flash look pleasing is bouncing, where you aim the flash head at a reflective surface (usually a ceiling or wall). To be able to choose the direction of the light, you have to choose your bounce surface, and tilt and swivel determine your freedom to do that. Full 360° swivel gives you full freedom; 270° swivel removes 25% of your choices, and depending on how you rotate into portrait orientation, could remove 50%.
The second reason swivel freedom is important is if you're going to use an optical triggering system for using the flash off-camera. The sensor for this is typically in the body, and it needs to be pointed towards your optical master unit (e.g., the camera's pop-up flash or another light in the setup). If you have full swivel, the head can always point where you want the light to go while the body faces the camera.
Zooming on the flash head simply means that the flash tube in the head can move back and forth so that the spread of the light will more closely match the field-of-view angle of the lens you're using. You can use this feature off-camera to adjust how focused the beam is. The longer the zoom setting, the farther back in the head the light sits, the more focused the beam is, and the farther the light can travel.
TTL, M, and Auto modes
TTL stands for "through-the-lens" metering. It's an automated way to set the flash's power output. The camera tells tells the flash to send out a "pre-burst" flash of a known brightness level; meters it, and then adjusts the flash's power based on the results and the flash's power limits. Just like using any metering-based auto mode on the camera body, it adjusts quickly and easily, but may not be perfect and you might have to dial in compensation. You typically use it for run'n'gun event situations where you move through different lighting situations without time to adjust.
Be aware that film-era speedlights typically do not work in TTL with digital SLRs; the algorithms based on film reflectance to calculate proper flash exposure had to be modified for digital sensors. Digital-era OEM flashes can typically switch between film and digital TTL, but film era flashes, obviously, only work accurately for film.
M, like M on the camera, is full manual mode, where you can directly set the flash's power output as a ratio of the full power. The ratios are most commonly given in full stops (1, 1/2, 1/4, 1/8, etc. etc). And, just like using M on a camera, you use this for consistency from shot to shot and precision of control. It's most commonly used for studio situations where the lighting is controlled and unlikely to change rapidly without a chance for retakes. The wider the range of settings, the more control you have over the flash's output. 1/128 power, for example, can be very useful when working close in for macro or product work because of the inverse square law. M also becomes very important as the only way to control the flash's power output if you're using manual-only radio triggers for off-camera flash.
Auto is a different way to automate the flash's light/power output that doesn't require TTL communication with the camera, so can be found in older film-era and manual-only 3rd party flashes. A sensor on the flash (typically an autothyristor) is used to cut off the flash output at the appropriate time. You may have to input the aperture and iso settings used for the shot into the flash.
High-Speed Sync/Focal Plane Flash
Most system cameras use focal plane shutters these days. Your shutter speed is determined by how big the gap between the 1st and 2nd shutters are as they sweep across the sensor. At a certain shutter speed, that gap becomes smaller than the sensor itself. And because most flash bursts are going to be much faster than the shutter speed, if you go higher than that shutter speed, the curtains will cover parts of the sensor when the flash goes off, and you'll get black bars at the top and/or bottom of the frame. That magic shutter speed is body-dependent and is known as the "maximum sync speed" of the camera (typically around 1/200s for most dSLRs).
High speed sync (HSS or FP) is a way to overcome this limitation, but requires proprietary brand-specific communication between the flash and camera hotshoe, so 3rd party flashes are less likely to include it. In addition, entry-level Nikon bodies cannot do it. But the camera tells the flash to act like a continuous light source for the duration of the exposure, and the flash pulses to do so. The cost of the rapid pulsing, however, is a power loss of roughly two stops.
This is most typically used when you want to use fill flash for portrait work with a shallow depth of field in bright sunlight. In sunny-16 conditions, (iso 100, f/16, 1/100s), if you want to use a larger aperture, you have to increase your shutter speed. You could also use ND filters instead of HSS.
The Strobist way of studio-style lighting with off-camera speedlights has become widespread, and you may be bitten by the bug. So, consider how many ways a flash lets you pop it when it's not on the hotshoe. The following features to look at are:
- PC (Protor-Compur) sync port [typically only on higher-end flashes]
- 1/8" (or 3.5mm) minijack sync port--like headphone jacks [3rd party only]
- proprietary wireless (TTL) slave mode [Canon: wireless eTTL; Nikon: CLS]
- "dumb" optical slave mode [Nikon: SU-4 mode; 3rd party "optical slave" modes]
- built-in radio receiver [TTL w/Canon RT gear; manual-only with most 3rd party flashes]
The main distinctions here are how many signals are communicated from the camera to the flash (full hotshoe protocol or only the sync signal), and the mechanism by which they're communicated (radio, optical, cable).
For example PC and 1/8" jacks can be used with cables for manual-only triggering; or as a way to connect a manual radio trigger without using the hotshoe. The camera hotshoe and the flash's hotfoot can be tethered with a TTL cable for full communication.
When a triggering system is labeled as "TTL" that doesn't just mean you can perform TTL over the system, but that the whole hotshoe signaling protocol can be used. Theses systems allow you to remote control the flash and do anything with it remotely that can be done on the hotshoe (or at least most of it). Triggering systems that are "manual only" can only tell the flash to fire in sync with the exposure being made.
Triggering systems that are "optical" use light. Proprietary TTL optical systems translate the hotshoe protocol into light signals; while "dumb" systems use a sensor on the flash to sense when another flash has gone off as the time to fire. Optical systems are limited by "line of sight" (the sensor has to "see" the master signal), and ambient lighting conditions (the more light there is, the more the signal can be overwhelmed).
Radio triggering is unhampered by line-of-sight or ambient lighting conditions and have better range and reliability, but is rarely built into a flash (though that seems to be changing).
Battery Pack Port
Speedlights have only four AAs in them. In heavy use, those AA batteries may have to be replaced multiple times, so an external battery pack can come in useful. Also, a larger power source can reduce recycle time (but bring a higher risk of overheating).
You have your eye on that super-cheap Yongnuo, right? While it might make sense, just understand what you're giving up by going with the lower pricetag. Build quality, copy consistency, and component quality are likely to be more variable than with OEM. Support, warranty, and resale value are likely to be of much lower quality. And future/backwards compatibility is likely to be lower.
Most 3rd party manufacturers reverse-engineer the hotshoe communication protocol, and as a result, while the flash may work very well with a current camera model, it may not work as well with a future or older model or, say, a film body with what is ostensibly the same flash protocol. To ease this issue, some 3rd party flashes can upgrade their firmware (Metz, Nissin). Some (Yongnuo) cannot.