I hear people talking about groups and elements in lenses, but I am not sure what they mean. Could someone please explain?
Except for a few budget cameras of the past, all camera lenses are made using at least two or more separate lenses. Each of these “thin” lenses is termed an “element”. In optical jargon, when individual lens elements are combined, the pair is called a “component”. Thus the typical camera lens contains several components. The elements that make up a component are usually, but not always, cemented together. Several components make up the compound camera lens. Components are generally not in contact with each other. Between them is an “air-space”. The air-space is also lens shaped, and thus it acts as a weak lens. The synonym for component is "group".
Such a complex mix of elements and components are needed to mitigate defects that prevent the lens from making a faithful image. We are talking about aberrations. There are seven aberrations, two induce color errors, five induce blur and/or distortions.
A group is two glass elements cemented together. This avoids the air to glass boundary between them. The two different elements have different index of refraction (affecting color wavelength differently). More elements are used to correct more aberrations.
The most simple "lens" is a single element lens, like a simple magnifying glass. But it is a poor lens, with serious optical problems, it cannot even focus different colors in the same place (called chromatic aberration). So a "doublet" or a two element group (of two different index of refraction) is a much better lens, it corrects for two colors (but not for three). How it does this is shown here:
The third one on the right shows two elements in one group.
But very much more can be done if we are critical. Maybe five elements makes a decent prime lens (a longer one), but when we make it zoom over a range, including wide angle, and add internal focusing, the $2000 lenses are often more than 15 elements. We certainly do consider them improved.
Honestly I ignore them. There is no provable correlation that have more elements and groups mean anything when it comes to image quality.
That being said, to answer your question:
- A lens element is a single lens in the traditional non-photography meaning of lens. It bends light in a certain way depending on its shape and material. Most lens elements are made of glass. They can also be made of fluorine (or is that fluorite?), ceramic or plastic.
- A group is one ore more lens elements which are moved together when the lens is focused or zoomed. Sometimes there is space between such elements but sometimes they are in contact.
Logically, you cannot have more groups than elements. So you can have a 16 element lens with 6 groups but not a 6 element one with 10 groups. Generally, more elements and more groups means that the design is more complex. These elements are there to correct different types of aberrations which can help improve performance. It can also allow lenses to have a longer zoom, closer focus range or higher magnification which is why more elements to not necessarily means better output.