As I understand it, the question is, what would happen to your molecule's stereochemistry if one hydrogen in a collection of hydrogens in identical environments was changed to something else?
The possibilities are:
1) that there is no change - replacing either hydrogen leads to identical molecules. Homotopic.
2) that you form enantiomers - replacing one hydrogen gives an S isomer, replacing the other gives an R isomer from something that wasn't previously chiral. Enantiotopic.
3) that you form diastereomers from a molecule that already has a chiral center - for example, replacing one hydrogen gives an R,S isomer and replacing the other hydrogen gives an R,R isomer. Diastereotopic.
Why does it even matter?
1) Homotopic hydrogens will react identically regardless of the steric effects of any reagents or solvents.
2) Enantiotopic hydrogens will usually react identically, but may be induced to react differently by providing a chiral environment - this can be done with chiral solvents, chiral salts, or chiral additives, and may allow you to specifically replace a single hydrogen to give a chiral product.
3) Diastereotopic hydrogens can sometimes react differently in achiral solvents with achiral reagents, due to the fact that the rest of the molecule is providing the chirality. The pair of diastereotopic hydrogens is chemically different, due to the three dimensional structure of the rest of the molecule.
So for example, the three hydrogens on the methyl groups of methyl ethyl ketone are homotopic - there is no way to selectively react with one of the three hydrogens, they are chemically indistinguishable in any environment. The methylene group, however, has two enantiotopic hydrogens - if you change one of them, you make an S enantiomer, if you change the other you make an R enantiomer. If you are really clever and use the appropriate chiral reagents, it is possible to selective replace only one of the two hydrogens, making only the
R product for example, instead of a racemic mixture.