Missions are objectives displayed at the top of the screen, you need to clear them in order to unlock the next farm, each farm will have a minimum number of missions, when you choose to go to the next farm is up to you! It definitely wouldn't hurt to clear more missions for extra rewards before moving on.
There is a progress bar showing you how many missions needed for progression. The reward you will receive is at the bottom right of the Quest.
There are several types of missions: Collecting cash, raise makers' level, automate makers, promote Characters/Makers, spend cow coins, get cards, earn cow coins.