Functional groups are basically what gives molecules their properties. Having certain atoms in certain configurations affects what a molecule can do, or how it behaves. Think about water: having oxygen (super greedy for electrons) bonded to hydrogen (not too attached to its electrons) resulted in a polar bond. That polarity resulted in water behaving in such amazing ways.
Other molecules are similarly determined by their functional groups. You do not need to memorize these functional groups, but you will be encountering them often, and so it is good to expose yourself to them as often as possible. This is not at all a complete, comprehensive list of functional groups. This is just a sample.