What is Insertion and β-hydride elimination?

In a migratory insertion, an unsaturated ligand (alkene, $\ce{CO}$) bound to the metal inserts into a cis M–H or M–C bond: $\ce{M-H}$ and an alkene give an alkyl $\ce{M-CH2-CH2-H}$; $\ce{M-R}$ and $\ce{CO}$ give an acyl $\ce{M-C(=O)R}$. A $\beta$-hydride elimination is the reverse of an alkene insertion: a hydrogen on the carbon $\beta$ to the metal moves onto the metal, releasing an alkene.