First of all, welcome to Smogon Jeff!
Now I will try to answer your questions because I can see where you're coming from and I don't want you to get the wrong impression of what's going on here. In addition to what I'm going to say, there are several excellent resources on Smogon's main site that probably explain things better than I could, so be sure to read those, starting with this one:
http://www.smogon.com/dp/articles/intro_comp_pokemon
(1) The tiers in a nutshell: we start with standard. Pokémon that are too strong for this tier are banned to Ubers, where anything goes. It is technically a banlist and not a tier, but there is a recognized Uber metagame, ladder, etc. Pokémon that are used in at least 1 out of every 20 battles on the standard ladder are called "overused" or OU. The determination of the OU list is a little complicated, and I'm sure there's an article about it somewhere, but basically it boils down to a cutoff of ~3.42% usage on the ladder. Everything not in Ubers or OU is then eligible for UU or "underused" play - the same cutoff applies for the UU list and Pokémon voted too strong for this tier are put on the BL list. So the three main competitive metagames are OU, UU and Uber (there are only about 6 or 8 BLs so the BL metagame doesn't really exist).
(2) The server statistics - Again I will try to be brief, but there is lots and lots to discover here. Each month, DougJustDoug runs a program to take all the data pertaining to every single battle fought on the Smogon University server and churn out what you see on page 1 of this thread. You can see how many times each pokemon was used on a given ladder, what its common moves and items were, and pretty much everything else you might need to know about the status of the metagame. Obviously people will use what makes them win, so it's an objective view of what is "best" (although this is only true in a veeery general sense). Hence, what is most popular is popular for a reason, although there are exceptions *cough* Electivire at #34 *cough*. There's no reason not to use whatever you want to, but the stats are a great way of seeing trends in the metagame so you can try to make the best team possible, which will usually end up being 6 OUs in OU if you are really serious about reaching the top of the ladder.
To sum up: the tiers really do measure popularity (at least OU and UU do), but that's all they do. Use whatever you want - what often separates the good from the best is the ability to use unorthodox sets to "counter the metagame." Hopefully that clears things up a bit for you; if not, all I can say is lurk more and ask more questions!