There are currently 1450 Levels in the game.
The levels show your progress in the game.
The more you progress through the game, the more you unlock, more gifts to send, extra land unlocked, more items to purchase in the store and access to more features of the game.
Your level is shown at the top of the game screen in the oval. Just to the left of that is your XP (experience points). If you are below level 501 the name for the level is also displayed below the XP bar which shows your progress to the next level. If you hover over the XP amount a small window will drop down showing your XP amount and how many you need to reach the next level. When you are at the top level the progress bar does not move, even though you are still earning XP, and you will not see how many needed to reach the next level as there aren't any until more are released.
This is an example of Level 302 with 8482450 XP
You will also earn Farm Cash every level which can be used to by luxury items in the game like bigger tools to work farms.