Airline alliances have several benefits for both the airlines and passengers. By working with other airlines, an airline can expand its route network to be much larger than what would exist with any one airline.
When things go wrong, an airline that’s part of an alliance has more options; for example if you miss your connecting flight on United, you could be put on the next flight operated by any of their alliance partners that gets you where you need to go.
Airline alliances also allow bag interlining (you can check your bag with Delta and it’ll be checked through to your connecting flight with Air France, for example), and they allow you to use your points accumulated on one airline to travel on an allied airline. Plus, you'll still earn miles with your airline of choice. Finally, you'll have access to other airlines' lounges. For example, oneworld elite members have access to over 650 airport lounges around the world.