The sugarsglucose 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 α-D-glucopyranose and β-D-mannopyranose are epimers because they differ only in the stereochemistry at the C-2 position. The hydroxyl group in α-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 not mirror images of each other, are also 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.