Why do I need to check-in for the flight?
By checking in customer confirms his/her presence on a flight. By asking customers to check-in e.g. latest 45 min or 1 h before departure, airline knows how many people are actually going to fly, how much fuel is needed, whether all the baggage has been loaded, how much food and drinks to load, etc. When all the preparations are done in advance, flights can depart on time.
From customer's point of view check-in's main function is to assign customer with a seat unless the seat has already been selected, accept baggage that is to go in the aircraft's cargo hold and to issue a boarding pass. A boarding pass is essential, because due security reasons you cannot go through security check without a boarding pass with a name that matches the one on your passport/photo ID.