Smogon University (or just Smogon) is a Pokémon website and community specializing in competitive battling. It has guides on battling strategies and the largest competitive battling forum on the internet. The website was founded by 'chaos' in 2004.
Smogon have created their own tiers, in which they rank Pokémon based on their usage. Each tier doubles as a playable battle format, which allows less-viable Pokemon to shine. For example, "NU" (NeverUsed) is the second-lowest tier, so the Pokemon there are relatively poor. In the NU battle format, you can only use Pokemon rated NU or below.
Smogon-based battle formats are played using battle simulators. Pokémon Showdown! is Smogon's official battle simulator, created by 'Zarel'. It also supports "official"/ cartridge formats.
Smogon have also set specific rules/clauses that players can abide by in the game to make the game more fair. These clauses are present on their battle simulator Pokémon Showdown, and give another point of difference to the real cartridge games. An example of a rule/clause is "Sleep Clause", which prevents you putting more than one of the opponents Pokémon to sleep.
Smogon and Pokémon Showdown 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, Pikalytics and Serebii.