And you are playing against LIVE people right, not AI?
Yes, competitive matchmaking mode is 5v5 Terrorists vs counter terrorist it is first to 16 round wins, Terrorists have to plant a bomb at either A site or B site. Counter terrorist team has to defend A site and B site from the terrorists. If the bomb is planted CTs have 30 seconds to retake the bomb site and diffuse the bomb. Diffusing takes 10 seconds without a diffuse kit, 5 seconds with one. If you die during a round, you do not respawn until the next round. In order to make sure you aren't playing with people who are TOO good it has a ranking system based on your wins and losses so you will be matched with similar ranked teammates.
CSGO is partly about aiming and recoil control, partly about movement and game sense, and lastly communicating with your teammates.
There is also 10v10 casual mode which is just a random lobby of 20 people, more lower skilled players and a lot more targets to shoot at than 5v5 competitive mode so casual can be fun to practice in.
Lastly there are other casual game modes of "arms race" which is similar to call of duty's "gun game". And then there is deathmatch which is essentially a free for all, no rounds and respawning is on, so you just run around getting kills, it is mainly used for aiming practice.
There is an offline mode with AI, but the AI tend to go from stupidly retarded oblivious AI, to they have wall hacks and are pulling off impossible shots from across the map.