VIP is a feature that let's you activate boosts for your Empire for a set period of time. These boosts are only active while VIP is enabled. You will often get VIP activation items as rewards.
The VIP level will grow as you accumulate VIP points, which are acquired as rewards for various upgrades and activities. The VIP level determines what boosts you receive while VIP mode is active and is cumulative for each level. Often boosts help economics or attack power while other boosts give additional quests (there is also an entire VIP quest line that only activate while you have VIP enabled). Once you hit level 20, you will also start receiving somewhat useful features to the game.
VIP Level Requirements
Note: The values below are cumulative and not how much you need each time (whew!).