1. DNA synthesis: This is the primary function of DNA polymerase. It adds nucleotides to a growing DNA strand, using an existing strand as a template. It does this by catalyzing the formation of phosphodiester bonds between the 3'-hydroxyl group of the last nucleotide on the growing strand and the 5'-phosphate group of the incoming nucleotide.

2. Proofreading: DNA polymerase has a built-in "proofreading" mechanism that checks for and corrects errors during DNA replication. This ensures that the newly synthesized DNA strand is a faithful copy of the template strand. If the polymerase detects a mismatch, it can remove the incorrect nucleotide and insert the correct one. This error correction ability is crucial for maintaining the integrity of the genome.

These two functions work together to ensure the accurate replication of DNA, which is essential for cell division, growth, and development.