Wiktionary
n. (context chemistry English) any of many classes of reaction in which an atom or bond moves or migrates from a site in a reactant molecule to a different site in a product molecule
Wikipedia
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. In the example below the substituent R moves from carbon atom 1 to carbon atom 2:
${-}\underset{| \atop \displaystyle \color{Blue}\ce{R}}\ce{C}\ce{-C-C- -> {-C-}}\underset{| \atop \displaystyle \color{Blue}\ce{R}}\ce{C}\ce{-C}{-}$Intermolecular rearrangements also take place.
A rearrangement is not well represented by simple and discrete electron transfers (represented by curly arrows in organic chemistry texts). The actual mechanism of alkyl groups moving, as in Wagner-Meerwein rearrangement, probably involves transfer of the moving alkyl group fluidly along a bond, not ionic bond-breaking and forming. In pericyclic reactions, explanation by orbital interactions give a better picture than simple discrete electron transfers. It is, nevertheless, possible to draw the curved arrows for a sequence of discrete electron transfers that give the same result as a rearrangement reaction, although these are not necessarily realistic. In allylic rearrangement, the reaction is indeed ionic.
Three key rearrangement reactions are 1,2-rearrangements, pericyclic reactions and olefin metathesis.