migratory insertion
Picture two passengers sitting next to each other on a metal's bench: one is a small group already bonded to the metal, say a hydride or a methyl, and the other is a flat ligand like a carbon monoxide or an alkene. In migratory insertion, the small group slides over and bonds to the neighbour, so the two fuse into one longer ligand that stays attached to the metal — and crucially, the seat the migrating group left behind is now empty. The chain on the metal has grown by one unit and a coordination site has opened.
Concretely, consider a metal bearing both a methyl group and a CO. In migratory insertion the methyl migrates onto the carbon of the CO, producing an acetyl group, CH3CO, bonded to the metal through its carbon; the two ligands have become one. The key bookkeeping points are that the metal's oxidation state does not change (no bond to the metal is broken homolytically the way it is in oxidative addition), but the total electron count drops by two and a vacant site appears, because what were two ligands are now one. Insertions come in flavours: a 1,1-insertion, as with CO, puts the migrating group on the same atom; a 1,2-insertion, as with an alkene, puts a hydride or alkyl on one carbon while the metal bonds to the adjacent carbon, growing an alkyl chain. The reverse of the alkene case is beta-hydride elimination.
Migratory insertion is the bond-building heartbeat of catalysis. It is how polymerization chains grow, one alkene at a time inserting into a metal-carbon bond in Ziegler-Natta and related catalysts; it is how the carbon skeleton is lengthened by a carbonyl in hydroformylation and the Monsanto acetic-acid process. The honest subtlety hidden in the name is that, despite the word insertion, the alkyl or hydride usually does the moving onto the stationary CO or alkene, rather than the unsaturated ligand wedging itself into a metal-alkyl bond — which is why the more careful term is migratory insertion.
In CH3Mn(CO)5, one CO and the methyl are neighbours. The methyl migrates onto a CO carbon to give the acetyl complex CH3C(O)Mn(CO)4, with a vacant site that a fresh CO then fills. The metal stays Mn(I) throughout; only the electron count and a free site change.
A metal-bound group migrates onto a neighbouring CO or alkene, fusing two ligands and opening a site.
Migratory insertion does not change the metal's oxidation state, unlike oxidative addition; and despite the name it is usually the alkyl or hydride that migrates, not the CO or alkene that inserts itself.