Smogon University, commonly shortened to Smogon, is a Pokémon website and community specializing in the art of competitive battling. It offers guides on battling strategies for people of different Pokémon knowledge backgrounds. The website was founded by 'chaos' and is a considerably well-known website, visited by competitive Pokémon battling enthusiasts.
Pokémon Showdown! is Smogon's official battle simulator created by one of the site's administrators: Zarel.
Smogon have created their own "tiers", in which they rank Pokémon in these tiers based on a Pokémon's usage and how powerful the Pokémon is, these tiers are designed to make the game more fair for players, as for example it's not very fair if your opponent is using fully fledged Legendries such as Mewtwo, Ho-Oh and Arceus etc. and you're using Pokémon such as Pikachu etc.
Smogon have also set specific rules/clauses that players can abide by in the game to make the game more fair, these clauses are also present on their battle simulator Pokémon Showdown, however it isn't a choice whether you can abide by them or not or their battle simulator. An example of a rule/clause is "Sleep Clause", Sleep Clause prevents you putting more than one of the opponents Pokémon to sleep, as it wouldn't be very fair if your opponent had a Darkrai and he used Dark Void to put all your Pokémon to Sleep, so that why they introduced "Sleep Clause" as a counter measure to stop that from happening.
Smogon and Pokémon Showdown are very technical as they have researched the game mechanics of the Pokémon Games and have adapted that in their battle simulator. They have many forums designed to help players play competitively and even have damage calculators to access the range of how much damage a Pokémon can do to another. They take into consideration entry hazards, weather, items etc. They also have a mentoring program designed to tutor new players and help them play at a competitive level.
Smogon is one of the main Pokémon Websites that people use along with the DB (everyone cheers!), Bulbapedia and Serebii.