Gly and Ser are often included in the fusion protein linker sequences to provide additional flexibility of that region. Gly residue in particular will ensure that the linker region is flexible and not folded in a difficult to access secondary structures. Note that linker sequences often contain protease recognition sites for ease of Tag removal. This is to ensure that the protease recognition site is bound by the protease efficiently. The disadvantage of such flexible linkers between your protein of choice and a Tag is that sometimes it may lead to unwanted fusion protein digestion in the cell during expression, but with that said, commercial vectors have linker sequences optimized to minimize such adverse effects.
Hi, in addition what they said above, the Ser residue gives some polar character to the linker in order to improve solubility and prevent aggregation problems.