A music synchronization license - or sync license, for short - is a music license that allows the license holder to "sync" music to some kind of media output. Often sync licenses are used for TV shows and movies, but any kind of visual paired with sound requires a sync license.
A sync license gives you the right to use a song and sync it with a visual in that when you hold a sync license, you are allowed to re-record that song for use in your project. If you want to use a specific version of the song by a specific artist, you also need to get a master recording license. Typically, a sync license is obtained from a music publisher while the master recording license is obtained by from the record label or owner of the master.
A sync license covers a specific period of time, and the license will stipulate how the song can be used. There is one flat fee involved in obtaining a sync license, and once the license is in place, the song can be used as stipulated as many times within the license period as the license holder likes. In other words, if you obtain a sync license and use the song in a film, you do not have to pay a fee on the sync every time the film is viewed.