Envision a filing cabinet. Your scanner would be that filing cabinet (which holds lot of stuff). Each drawer would be comparable to a system. In each drawer you have file folders, which would be groups. In each file folder you have individual things and in scanners these things are frequencies or talkgroups depending upon the type of system you are interested in listening to.
How much of what kind of stuff you put in each file folder (or group) is your choice (the maximum limit escapes me now).
How many file folders (groups) you have in each drawer (system) is your choice, up to a maximum of 20.
That's a long way of saying a system is a big container of "radio stuff" and groups are smaller containers within that big container.
Sites are a little more difficult to explain and the "depends" word applies. If what you want to listen to is a conventional radio deal (as in not a trunked thing), then sites don't matter.
(I'm trying to avoid the word "system" here, so as to avoid confusion. "System" in the context of that what you are wanting to listen to is different than "system" when it comes to programming a scanner. Same word but means two separate things, in other words).
Having mentioned the explanation for my choice of words, now on to when sites may be applicable: If what you want to listen to is a "trunked radio system". Radio systems for small geographic areas usually have a single site. For larger areas, such as the state of Connecticut, there are multiple sites all working together to provide a communications network for the users of the system. As the users travel from one area to another, their radio communications are handed off from one site to another, just like cellular telephone roaming.
For the scanner listener, the only sites that need to be programmed in a scanner are those sites the scanner is likely to be within 30 miles of.
Your best bet is to get programming software for your computer to program your scanner (Freescan or ArcXT which I use). If you are a database subscriber, the software will grab all the stuff needed to program your scanner. It makes life a lot easier because it sets up the system and sites (when needed and how needed) as well as groups within the system. A lot of guesswork is taken out that way.