PS Plus gives you 2 free games to play with each month. You can keep playing them so long as your PS Plus membership is still active. In December 2013, PS4 owners could download Resogun and Contrast free of charge. You also get 2 free games for the PS Vita and PS3 platforms.
PS Plus is required to play your games online, or to download select game titles or add-ons at a discount from the PS Store. Soon enough it will also allow you to store your game saves on cloud storage.