A cover song is a new recording of a composition that you did not write or of which you do not have legal ownership, such as an a cappella recording of "Poker Face" by Lady Gaga.
To distribute a cover song in the United States, you need to procure a mechanical license. Find out more details on how to do so here.
If the composition that you are trying to cover is in the public domain, you do not need to request a mechanical license.