The Pharisees are one of three major sects of Judaism in the Second Temple period (530 BCE-70 CE): the Pharisees, the Sadducees, and the Essenes. There's also a mysterious "fourth way" philosophy that Josephus, the Jewish historian, links to Judas the Galilean's abortive revolt in 6 CE and then blames for the Jewish War of 66-70 CE (c.f. Josephus' The Jewish War).

Our sources for the Pharisees are notoriously thin, as with most information about the Second Temple period. We're largely dependent on Josephus, the New Testament, and to lesser extents, the Talmud and the Dead Sea Scrolls.

Pharisaic Beliefs

The Pharisees, unlike their counterpart the Sadducees, famously held to the resurrection of the body, an immortal soul, and a Messianic age that was yet to come. Beyond this, they believed that an oral tradition had been given to Moses at Sinai, and that it was guarded and kept by a series of elders (Mishnah Aboth 1:1).

In addition, if the NT can be believed here, the Pharisees apparently had a routine of praying in a public setting, in fairly ostentatious ways. Whether or not this is actually the case seems very difficult to determine, as our sources are incredibly limited here.

What else did they do?

After the destruction of the Second Temple (70 CE), the Sadducees basically ceased to exist. This is largely a function of two elements, one is that the Sadducees are far more involved in the cultic practices of the Temple (that is, the day to day operations, rather than the non-technical sense in which the word is now used). Second, the Pharisees seem to play a large role in the creation of Rabbinic Judaism, which means they either marginalize or eliminate the Sadduaic viewpoint entirely. Edit: I should've mentioned that the Sadducees also played a significant role in starting the Jewish War. However, we have to keep in mind that Josephus himself is a Pharisee, and has some degree of hostility towards the Sadducees.

In essence, they're very important for understanding how Rabbinic Judaism came to be, and more importantly, how it took the shape that it did.

Suggested Reading:

Cohen, Shaye J.D.: From the Maccabees to the Mishnah

Grabbe, Lester: An Introduction to Second Temple Judaism

The Pharisees were a political and religious group that were loosely in charge of Israel's religious practices during the second temple period. This post on /r/AcademicBiblical gives a good overview of some of the beliefs of the Pharisees versus the other main religious/political group at the time, the Sadducees.