Migratory aptitude is the relative ability of a migrating group to migrate in a rearrangement reaction

Rearrangement reaction

A rearrangement reaction is a broad class of organic reactions where the carbon skeleton of a molecule is rearranged to give a structural isomer of the original molecule. Often a substituent moves from one atom to another atom in the same molecule...

. This can be affected by the leaving group (whichever gives a more stable carbocation

Carbocation

A carbocation is an ion with a positively-charged carbon atom. The charged carbon atom in a carbocation is a "sextet", i.e. it has only six electrons in its outer valence shell instead of the eight valence electrons that ensures maximum stability . Therefore carbocations are often reactive,...

) and the group that 'stays' (whichever can stabilize the positive charge best).It also depends upon the electron density of the migrating group i.e.
Hydride > tert-alkyl > sec-alkyl = phenyl > primary alkyl > methyl>H

The Migratory aptitude is used in reactions such as Pinacol-PINACOLONE rearrangements, etc...........