Generally this topic is discussed when covering tandem mass spectrometry fragmentation and occurs generally by the same mechanisms.
For example, of a mechanism of alpha-cleavage, an electron is knocked off an atom (usually by electron collision) to form a radical cation. Electron removal generally happens in the following order:  1) lone pair electrons, 2) pi bond electrons, 3) sigma bond electrons.
One of the lone pair electrons moves down to form a pi bond with an electron from an adjacent (alpha) bond.  The other electron from the bond moves to an adjacent atom (not one adjacent to the lone pair atom) creating a radical. This creates a double bond adjacent to the lone pair atom (oxygen is a good example) and breaks/cleaves the bond from which the two electrons were removed.
In molecules containing carbonyl groups, alpha-cleavage often competes with McLafferty rearrangement.