The sugars glucose and galactose are epimers. In glucose, the -OH group on the first carbon is in the axial position, the direction opposite the -OH group on carbon C-4. In galactose, the -OH group is oriented in the same direction, the equatorial position. In cyclical compounds like these, the -OH group on C-1 may lie in opposite directions, as well. This structural difference distinguishes two anomers. The two molecules pictured are both epimers and anomers (as indicated by the α and β designation).
The stereoisomers β-D-glucopyranose and β-D-mannopyranose are epimers because they differ only in the stereochemistry at the C-2 position. The hydroxyl group in β-D-glucopyranose is equatorial (in the "plane" of the ring), while in β-D-mannopyranose the C-2 hydroxyl group is axial (up from the "plane" of the ring). These two molecules are epimers, but because they are not mirror images of each other, are not enantiomers. (Enantiomers have the same name, but differ in D and L classification.) They are also not sugar anomers, since the wrong carbon is involved in the stereochemistry.
Epimerization is a chemical process where an epimer is made to transform into its chiral counterpart. It can happen in condensed tannins depolymerisation reactions. Epimerisation can be spontaneous (generally a slow process), or catalyzed by enzymes, e.g. the epimerization between the sugars N-acetylglucosamine and N-acetylmannosamine, which is catalyzed by renin-binding protein.