Since this list is so incredibly extensive I won't go into much detail.
Sweepers are fast and powerful, supposed to dish out damage and escaping afterwards.
Walls are supposed to take a lot of hits whilst withering down the opponent whilst supporting the team with various strategies.
Leads are supposed to set up as much possible, prevent opposing setup and switch out as little as possible.
Tanks are bulky Pokemon with attack and defence, but often lacking in speed.
Gimmicks/Trolls are Pokemon using a very specific set to throw of the opponent.
Support Pokemon are supposed to heal and keep a team going with various healing moves.
Here is a more in depth list of roles.
Tiers are fan made tiers. By tier I guess you could call them categories for Pokemon. They are used for competitive battling to split each Pokemon up based on how they fair in each tier. (Source)
Ubers is the highest battling tier. Anything can be used here.
OU Pokemon that are really good, just not Ubers, go here.
The Pokemon in UU are still good, but they have some sort of shortcoming preventing them from excelling.
RU is quite like UU, only slightly weaker.
There are some decent Pokemon in NU, but a whole lot of rubbish junk as well.
In LC, only first stage evolution Pokemon are allowed here, a parallel metagame if you will.
There are also two Borderline tiers in between OU-UU and UU-RU, containing Pokemon that's to strong for the lower tier but don't see enough usage in the higher tiers.
Monthly Metagames are new metagames that twist the rules of batteling in one way or another to create new strategies and threats.
CS=Clear Skies. A team that don't utilise weather.
Hail Team. A team using the Hail condition to stall and spam Blizzards.
Sun Team. A team that uses powerful Fire type attacks and Chlorophyll Pokemon.
Rain Team. A team that uses Water attacks, Thunder, Hurricane, Rain abusing abilities and the weakening of Fire moves.
Sand Team. A team that uses Rock/Ground/Steel types to avoid damage.
Trick Room Team. A team that uses the move Trick Room to turn slow and powerful Pokemon into fast monsters.
Tailwind Team. A team that uses the boost in speed from Tailwind to make medium fast Pokemon exceptionally fast.
HO/Hyper Offensive team. A team with majority powerful sweepers and tanks and minimal defence.
Stall Team. A team focused on surviving as long as possible whilst taking out the for via indirect means.
Baton Pass Team. A team focused on accumulating stat boosts and then pass them to a powerful Pokemon using Baton Pass
Set up is when a Pokemon uses some form of boosting or support move to aid the team or sweep on its own.
Hazards are the moves Spikes, Toxic Spikes and Stealth Rock.
A core is a set of two or three Pokemon in a team that either work very well together or cover many of each other weaknesses creating a sturdy group of Pokemon that can be challenging to take down.
Synergy just means a team as a whole with the ability to cover each member's weaknesses and also have an answer to almost every Pokemon in the game. Source
Extra credit to Blobyolo, fizz and Linkpower for answers way better than mine.