The stereochemical term diastereotopic refers to the relationship between two groups in a molecule which, if replaced, would generate compounds that are diastereomers. Diastereotopic groups are often, but not always, identical groups attached to the same atom in a molecule containing at least one chiral center.
For example, the two hydrogen atoms of the CH moiety in (S)-2-bromobutane are diastereotopic.  Replacement of one hydrogen atom (colored blue) with a bromine atom will produce (2S,3R)-2,3-dibromobutane.  Replacement of the other hydrogen atom (colored red) with a bromine atom will produce the diastereomer (2S,3S)-2,3-dibromobutane.
In chiral molecules containing diastereotopic groups, such as in 2-bromobutane, there is no requirement for enantiomeric or optical purity; no matter its proportion, each enantiomer will generate enantiomeric sets of diastereomers upon substitution of diastereotopic groups (though, as in the case of substitution by bromine in 2-bromobutane, meso isomers have, strictly speaking, no enantiomer).
Diastereotopic groups are not mirror images of one another about any plane. They are always different, in any environment, but may not be distinguishable. For instance, both pairs of CH hydrogens in ethyl phenylalaninate hydrochloride (PhCHCH(NH)COOCHCH Cl) are diastereotopic and both give pairs of distinct H-NMR signals in DMSO-d at 300 MHz, but in the similar ethyl 2-nitrobutanoate (CHCHCH(NO)COOCHCH), only the CH group next to the chiral center gives distinct signals from its two hydrogens with the same instrument in CDCl. Such signals are often complex because of small differences in chemical shift, overlap and an additional strong coupling between geminal hydrogens. On the other hand, the two CH groups of ipsenol, which are three bonds away from the chiral center, give separate H doublets at 300 MHz and separate C-NMR signals in CDCl, but the diastereotopic hydrogens in ethyl alaninate hydrochloride (CHCH(NH)COOCHCH Cl), also three bonds away from the chiral center, show barely distinguishable H-NMR signals in DMSO-d.
Diastereotopic groups also arise in achiral molecules. For instance, any one pair of CH hydrogens in 3-pentanol (Figure 1) are diastereotopic, as the two CH carbons are enantiotopic. Substitution of any one of the four CH hydrogens creates two chiral centers at once, and the two possible hydrogen substitution products at any one CH carbon will be diastereomers. This kind of relationship is often easier to detect in cyclic molecules. For instance, any pair of CH hydrogens in cyclopentanol (Figure 2) are similarly diastereotopic, and this is easily discerned as one of the hydrogens in the pair will be cis to the OH group (on the same side of the ring face) while the other will be trans to it (on the opposite side).
The term diastereotopic is also applied to identical groups attached to the same end of an alkene moiety which, if replaced, would generate geometric isomers (also falling in the category of diastereomers). Thus, the CH hydrogens of propene are diastereotopic, one being cis to the CH group, and the other being trans to it, and replacement of one or the other with CH would generate cis- or trans--2-butene.
 Diastereotopicity is not limited to organic molecules, nor to groups attached to carbon, nor to molecules with chiral tetrahedral (sp-hybridized) centers: for instance, the pair of hydrogens in any CH or NH group in tris(ethylenediamine)chromium(III) ion (Cr(en)), where the metal center is chiral, are diastereotopic (Figure 2).
The terms enantiotopic and diastereotopic can also be applied to the faces of planar groups (especially carbonyl groups and alkene moieties).  See Cahn-Ingold-Prelog priority rule.