A cover song is a new recording of a song that was previously written, recorded and released by someone else.
When you record a cover song, you're recording your own version of someone else's copyrighted song. While you may own the cover of "Roar" that you painstakingly recreated in your home studio with Asiatic flutes and a sitar (and without Katy Perry), someone else still owns the rights to the song itself -- the lyrics, melody and song structure.
Licensing the song enables you to legally sell your song in stores like iTunes and to promote your cover recording without worrying about getting a cease-and-desist notice or waking up to discover that your track has been abruptly yanked from all platforms. It also makes you an awesome person because you'll have done your part to ensure that the original songwriters get paid royalties for their work.