A mechanical licence is the agreement by which permission to reproduce a musical work on a sound carrier is granted by the copyright owner or its representative. “Mechanical” refers to the reproduction of copyrighted music in a “contrivance” for the “mechanical reproduction of music.” If this makes you think of music boxes, it’s because it is, admittedly, somewhat outmoded language. Nevertheless, “mechanical licence” is the customary industry term for such permission.
Such a licence is extremely specific: it is limited to a particular musical work, as reproduced by the user on a particular product. The licence is also specific as to the catalogue number of the product, the playing time of the recording and the performer.
Note that mechanical licences are not issued per album but, rather, on a song-by-song basis. If a product contains 10 songs, you must obtain permission for each one. Also because the ownership of a copyright can be divided between more than one owner, licences are required from all owners before the work is fully licensed.