Alpha-cleavage (α-cleavage) in organic chemistry refers to the act of breaking the carbon-carbon bond[1] adjacent to the carbon bearing a specified functional group.
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.
In photochemistry, it is the homolytic cleavage of a bond adjacent to a specified group.