Wall; A Pokemon that is meant to take either physical or special attacks over and over. (Do you know the difference between physical and special moves?) They often carry 1 or 2 offensive moves, a recovery move and a status move. The prime special wall is Blissey. She takes special attacks over and over and uses a recovery move so she can keep taking those hits.
Sweepers; These pokes are meant to just do damage to the opponents team, but that's about it. Their life goal is either kill or be killed. They almost never run a recovery move, and tend to have at least 3 attacking moves. The fourth move may be another attacking move but may be a move that boosts an offensive stat, such as swords dance, dragon dance or many others.
Tank; This is kinda a mix of a sweeper and wall. They are meant to take hits and hit back. They tend to not be as sturdy as walls and deal less than sweepers, but they can be a nice mix for any team.
Clerics are pretty much walls that carry moves like heal bell and wish. Heal bell will remove status from your entire team while wish heals whatever Pokemon is on the field next turn by half the original pokes health.
Type synergy can be meant in an offensive or defensive way. Offensively you will tend to look at a single pokemons moveset. You want to make sure that the pokemons moves will hit a wide variety of Pokemon and won't be walled by anything (aka the Pokemon can hit anything for neutral damage or better). An example of this is you have a Salamence with dragon claw. Dragon type moves are resisted by steel types. So you add earthquake to hit steel types and try it out in battle. Once you start the battle you realize your opponent has a Skarmory, which you cannot hit for neutral damage with those to moves due to it resisting dragon type moves because of its steel typing and being immune to ground types because of its flying typing. So for your next battle you add flamethrower, which gives you perfect neutral coverage with those three moves. For defensive Pokemon offensive move synergy is a little less mandatory
Defensively it means that your team covers each others weaknesses. An example of this is you have a Vaporeon, which is weak to electric and grass type moves. So a good Pokemon to use with vaporeon would be rotom's fire form, which resists both electric and grass type moves.