Illustrated Glossary of Organic Chemistry

Rearrangement: A mechanism step or reaction in which an atom or group migrates from one carbon atom to another. The reaction often includes the breaking and/or making of carbon-carbon sigma bonds.

Secondary carbocation
No resonance stabilization

Tertiary carbocation
With resonance stabilization
In this carbocation rearrangement, the methyl group migrates from one carbon to the adjacent carbon, causing a secondary carbocation (which lacks resonance stabilization) to rearrange to a tertiary carbocation that has resonance stabilization. Carbocation rearrangement is a mechanism step, and one of the three common carbocation fates.

This oxyCope rearrangement of hexa-1,5-dien-3-ol is a [3,3]-sigmatropic rearrangement, followed by tautomerization.

This Baeyer-Villiger oxidation reaction is a rearrangement reaction because the phenyl group migrates from the carbonyl group to an oxygen atom.