There are a few different map modes in Counter Strike: Global Offensive that you should know about. Each mode has different objectives and CS:GO is played by the round. Each round is quick, generally no respawns, and the performance of the players and the team determine the amount of cash you have next round to shop with, in addition to what weapons are carried over into the next round.
Most modes have the same basic principle, either wipe the enemy team or complete the objective first. Depending on your side, your objective will usually change from defending hostages and attempting to rig bombs (terrorists) or rescuing hostages and defending the bombsite. CS:GO features the Arsenal map modes, which bring the Gun Game mod to the main game.
In the mode, you are automatically given your weapons loadout each match (from the pistol up to the sniper rifle). Each round one team attempts to plant the C4 (randomly assigned) while the other team attempts to prevent it / diffuse the C4. There is only one bombsite as well, so the difficulty is dealing with the automatic weapons, lack of the shop, and playing a limited version of Bomb Defusal at the same time.
Arsenal: Arms Race
Based on the Gun Game mod, this mode has no shop. After a recent update, weapon randomization was added to this mode. Basically with each kill you level up the weapon you have, until you read the final weapon which is the gold knife. Killing a player with the gold knife wins the game for your team. The MVP becomes the "team leader" and will have a red or yellow glow to them, killing them will grant you an instant level up.
A classic CS mode, the terrorists spawn near a hostage and must prevent the counter-terrorists from rescuing the hostage and, also, avoid having their entire team wiped. In CS:GO there is only two hostages and hostage positioning is randomized.
The primary tournament mode. The terrorists need to plant C4 at a location often near the counter-terrorists spawn point. The counter-terrorists are tasked with preventing the attachment of the C4 to the bombsite, defusing the bomb, and surviving until the end of the counter. The terrorists need to plant the C4 and have it detonate and avoid losing every member of their team before the round ends. Either side claims victory if they wipe the other side (although terrorists get a small window for victory if they've planted the C4, if it still detonates even with their entire team dead, they get the point).
Pure DM fun. You spawn with a six second invulnerability timer to use the modified shop. Weapons are free, but certain accessories are not available (armor, nades, etc.). You get points for kills and assists. Bonus weapons randomly are enabled and you can press G by default to respawn. At the end of the match timer, the winner is declared based on most points.
That's the major map modes. Community servers have various mods, but generally speaking Bomb Defusal is the most popular (and balanced mode). So if you're just getting started, look into that one.