Specificity pockets are necessary to demonstrate substrate selectivity. Substrate selectivity for serine proteases is assured by having specific pockets that are only able to bind specific residue side chains, allowing proteolysis at the desired site. This is through having specific residues in the enzyme that are only capable of interacting with the desired amino acid. For example, hydrophobic side chains will line a specificity pocket for a hydrophobic residue; negative side chains will line the specificity pocket for a positive residue.
Enzyme function needs to be specific, without indiscriminate protein cleavage. Having a series of specific pockets either side of the scissile bond helps reduce the likelihood of untargeted proteolysis. However, with many proteases (such as thrombin) it is possible to cleave almost any polypeptide if enough incubation time is given. The risks of this can be reduced by having protease activation cascades, where a different protease is only expressed during a specific set of conditions to convert zymogen to its active form (such as chymotrypsin to trypsin).