The main areas of use are the conversion of ketones to esters (Baeyer-Villiger oxidation), epoxidation of alkenes (Prilezhaev reaction), conversion of silyl enol ethers to silyl α-hydroxy ketones (Rubottom oxidation), oxidation of sulfides to sulfoxides and sulfones, and oxidation of amines to produce amine oxides. The following scheme shows the epoxidation of cyclohexene with mCPBA.
The epoxidation mechanism is concerted: the cis or trans geometry of the alkene starting material is retained in the epoxide ring of the product.  The transition state of the Prilezhaev reaction is given below:
The geometry of the transition state, with the peracid bisecting the C-C double bond, allows the two primary frontier orbital interactions to occur: π (HOMO) to σ* (LUMO) and n (HOMO, regarded as a filled p orbital on a sp hybridized oxygen) to π* (LUMO), corresponding, in arrow-pushing terms, to formation of one C-O bond and cleavage of the O-O bond and formation of the other C-O bond and cleavage of the C=C π bond.