Diegetically, there are very few restrictions on elite battles in the Pokemon series. Want to compete for the title of champion with 6 literal gods? That's fine. Want to muscle your way through with Full Restores (items that fully heal your Pokemon and cure their status conditions)? Use as many as you can afford. The only real restriction on players independently battling with their teams is the inability to use items in battle and occasionally level equalization to 50. None of this, however, would make a particularly fun or long lasting competitive scene. If every game involved the same dozen or so most powerful pokemon, players' ability to use their favorite Pokemon would be severely restricted. Because of this, two independent metagames have evolved to try to bring some order and variety to a series which has 700+ creatures.
The first format is the typically much looser VGC (Video Game Championship). It is played in a Doubles format (using two Pokemon at once) with rotating restrictions, normally based around whatever the most recent games have been. They always have restrictions related to using multiple of the same Pokemon, but otherwise might ban certain particularly powerful Pokemon or restrict their usage to just one or two. The second format is the Smogon tiers. While not official, Smogon is the largest fan community and the center of the Singles competitive scene (using just one Pokemon on the field). While the Doubles format may allow some otherwise weak Pokemon to shine in teams built around them, Singles tends to be much harsher. However, there are some Pokemon who could never, in a minimally restricted field of play, be competitively viable.
Smogon bases its tiers on usage stats, with only occasional bans for Pokemon too centralizing to any given metagame. The tiers are PU (no acronym, the weakest), NU (Never Used), RU (Rarely Used), UU (Under Used), OU (Over Used, the "standard" tier), Ubers (originally just the OU banlist, now it's own tier populated by the strongest of the strong), and AG (Anything Goes, the Ubers banlist consisting of exactly one Pokemon). This is what "makes meta from madness," because segmenting Pokemon into tiers gives most of them a chance to be actually usable, allowing players to make teams with their favorite Pokemon. This also allows for layers of metagaming as each tier develops its own meta that changes over time, with even Pokemon in a given tier being more or less viable.
Smogon does not create this metagame from nothing. In order to track the usage of all Pokemon, it runs its own online battling simulator, Pokemon Showdown, in which players can create teams of Pokemon as they see fit, adjusting their IVs (genetics that effect stats, essentially), EVs (hidden values of experience that effect stats further), moves, held items, etc. Beyond all this it also has a strategy guide that covers nearly all Pokemon presenting commonly used combinations of EVs, moves, held items, and other options. It also developed the terminology used around the metagame, such as the distinction between "checks" (Pokemon that can beat another one, but only in certain circumstances) and "counters" (Pokemon that can stop another dead in its tracks) or "bulky water types" (Water typing being good defensively, and many Water types also possessing the correct combination of stats, moves, and abilities to take advantage of this) that don't exist in the single player portion of the franchise which can often be completed just by using the very first Pokemon you receive.