The wife of the first Hasmonean king, Aristobulus, who ruled from 104 to 103 BC. After his death, she married his brother Alexander Janneus, who was king from 103 to 76 BC. Their marriage was likely a "levirate" marriage (a Jewish custom where a man marries his deceased brother's widow under certain circumstances).
When Janneus died, Salome Alexandra became queen according to Alexander Janneus's will. She was the only Jewish woman to rule as queen in Judah, apart from the usurper Athaliah, who was queen from 841 to 835 BC.
Before he died, Jannaeus told her to make peace with the Pharisees (a Jewish religious group) who had fought against him. Salome followed this advice. It helped that her brother, Simon ben Shetach, was a well-known Pharisee leader.
Salome Alexandra ruled for almost 10 years, from 76 to 67 BC. It was a peaceful time during which the Pharisees gained significant power. Pharisees were allowed to join the Sanhedrin (the highest Jewish council) for the first time. By the time of Christ, the Pharisees had become almost as powerful as the Sadducees in the Sanhedrin.