BSA has traditionally been added to solutions to reduce or block unwanted interactions between assay components and between these and the surface of the sample container. BSA competitively bind surfaces and prevents enzymes (e.g., RE or DNA Polymerase) binding and being 'removed' from the reaction. Assay solutions often also include a weak detergent and other solvents which help limit unwanted interactions.
In the case of specialised PCR, further additives can be added to enhance DNA melting, primer hybridisation and DNA Polymerase activity.