How do geometric isomers arise?

A carbon centre bound to 4 DIFFERENT groups, i.e. #CR_1R_2R_3R_4# can exist as 2 non-superposable stereoisomers, such that given a pair of stereoisomers, one isomer is the mirror image of the other, and these so-called optical antipodes cannot be superimposed on the other.

The stereoisomers have identical chemistry in all respects, except when in a chiral environment. Should a second chiral centre occur in the molecule, 4 different stereoisomers are possible: #"RR; SS; SR; and RS"#. #"RR"# is enatiomeric to #"SS"# but DIASTEREOMERIC with respect to #"RS"# and #"SR"#.

Biological chemistry and especially the chemistry of enzymes are replete with examples of chirality, such that typically an enzyme, of a definite chirality, will only work on a particular biological substrate. Sugar, which most of us take for granted, is an example of these substrates. It has a definite stereochemistry, upon which only a particular handed enzymatic catalyst, a particular diastereomer, will operate.

A simpler example of diastereoisomerism occurs in the #"2-butylene"# molecule. Of course, you know that we could have #"trans-2-butylene"# versus #"cis-2-butylene"#. These are geometric isomers that are not mirror images, and are thus a simple example of #"diastereoisomerism"#. I urge you to read the relevant chapter in your text in order to consolidate your understanding.