Since no natural amino acids are strongly nucleophilic, the base in a catalytic triad polarises and deprotonates the nucleophile to increase its reactivity. Additionally, it protonates the first product to aid leaving group departure.
The base is most commonly histidine since its pK allows for effective base catalysis, hydrogen bonding to the acid residue, and deprotonation of the nucleophile residue. β-lactamases such as TEM-1 use a lysine residue as the base. Because lysines pK is so high (pK=11), a glutamate and several other residues act as the acid to stabilise its deprotonated state during the catalytic cycle. Threonine proteases use their N-terminal amide as the base, since steric crowding by the catalytic threonines methyl prevents other residues from being close enough.