I understand that the millimeter measurement on a lens is, for lack of a better term, how far it can "zoom" in or out, but what about macro lenses? What does the millimeter measurement signify? How can I tell which macro lenses will be able to zoom in closer than others, since the defining factor of a macro lens is how close it can zoom in, not how far?
A macro lens creates an image on the camera sensor/film that is at least as large as the object being photographed. The ratio of the subject size on the film/sensor plane to the actual subject size is called the reproduction ratio. Good macro lenses have a reproduction ratio of 1 to 1 or higher.
For example, if you are shooting a dime, a macro lens will create an image on your film/sensor that is the same size as the dime.
The focal length of your macro lens will essentially determine how far away you can get from your subject and maintain a 1:1 reproduction ratio. Shorter focal length macro lenses require you to be closer to the subject than longer focal length lenses. Also, longer focal length macros will have a shallower depth of field than shorter focal length macros.
Check out The Digital Picture for some examples and review of macro lenses
Macro lenses tend to come in fixed-focal length varieties, rather than "zoom" varieties. As such, there really isn't much in the way of zooming with macro photography...if you want to get closer, you have to physically move the camera and lens closer. When it comes to macro lenses, you are just as interested in magnification and minimum focus distance (MFD) as focal length.
To really do macro work, you need to first check the maximum magnification. Many lenses have tiny fractional magnification...0.15x, 0.2x, etc. A true macro lens will usually have a 1.0x magnification, and many close-up lenses can get you as much as 0.5x magnification. It is also possible to go beyond 1x magnification with a macro lens and some extension tubes or diopters...both devices that change your minimum focus distance.
Minimum focus distance is what determines how close you can get to your subjects. Most 1:1 (1.0x mag) lenses are only 1:1 at MFD, and that is usually pretty close. The ever popular Canon EF 100mm f/2.8 macro lens is a 1:1 macro lens, and the sensor is a mere 1 foot (305mm) away from the subject at full 1.0x (1:1) magnification. The lens itself is about 6 inches (152mm) long, and when mounted on the camera body, that only leaves a few inches of space between the front of the lens and the subject. Longer focal lengths, such as 180mm or 200mm, give you more working distance. Shorter focal lengths allow you to get in much closer.
Finally, focal length is an important factor as it affects the maximum amount of background blur. The longer the focal length is, when combined with an f/2.8 aperture (common for most true macro lenses), the better the background blur is due to background compression. A 180mm or 200mm macro lens will produce the most creamy background blur, while a 100mm lens will produce a blend of blur and soft detail. Shorter macro lenses, such as 50mm and 60mm macro lenses, will generally not produce as nice a background blur, but will function with far less working space. When you have to work within a confined space, say a museum to photograph art, a shorter focal length macro lens is often very useful.
When discussing macro capability, all modern* macro lenses do 1:1 magnification (with exception being the last generation of Sigma/Tamron that did 1:2 and and the special macro Canon 65mm that does up to 5:1). This magnification ratio is the 'zoom' you seek. 1:1 means the object will be represented in real life size on the sensor. If the object is 1cm across, it's relevant image circle portion on the sensor will take up 1 cm.
For a macro lens, the focal length (the millimeters marking) will determine your working distance (and your perspective at the minimum focus distance) - how far back you can be and still achieve that 1:1 ratio. A 40mm macro and 100mm will both magnify an object 1:1, but the 100mm lens will allow you to be further away while you do it. Moving closer with the 100mm (or any lens at its minimum focus distance) won't get you more than 1:1, it simply won't focus closer.
* I'm refering to lenses still being actively sold, which doesn't include older manual focus Nikon 1:2 lenses but does the Sigma 70-300mm f/4-5.6 DG APO Macro that is still active and does 1:2.