The Pharisees were a group of politically-minded religious people. It is their beliefs that have come down through the ages as modern Judaism.
For centuries, the Pharisees were rivals to the Sadducees. The Sadducees were priests and other upper class people, whereas the Pharisees were lower class. The Sadducees claimed many privileges for themselves, and this did not go down well with most people, so in the end they lost out to the Pharisees.
The Pharisees figure in the New Testament because they were in control at the time of John the Baptist and Jesus. The Apostle Paul may originally also have been a Pharisee. It was the Pharisees who were keen to see the back of Jesus as they saw him as a threat.