Goals are targets given to the player by Peck. They typically reward the players with XP and Gems once completed, though some also reward Stars. Completing goals are the best way to level up quickly given the experience rewarded, even if they can sometimes leave the player slightly out of pocket - the monetary reward for completing a furniture goal often doesn't completely cover the cost of purchasing the individual items necessary.
Primary goals often help introduce the player to new mechanics, especially towards the beginning of the game. Examples include planting seeds that have just been unlocked following a level up, purchasing and using furniture, and breeding or otherwise obtaining new types of Bunnies.