Aspasia was born in Miletus and must have belonged to a wealthy family, because her parents could afford an education for their daughter. In the early 440s, the family settled in Athens, where they were metics, i.e. non-Athenians living in the city. These people had to pay an additional tax and did not receive full political rights. An Athenian man could not have a full marriage with a metic; their children could not receive full citizen rights. Of course, these relations were not illegal either.
Aspasia was the metic lover of the Athenian politician Pericles, and gave birth to his son-without-full-rights, who was also called Pericles. In the later 430s, when the politicial opponents of the elder Pericles (a/o Hagnon) tried to accuse him of impiety, Aspasia was also mentioned as someone acting impiously, but she was not convicted. After the death of her lover in 429, Aspasia lived together with his friend Lysicles, but this affair was ill-fated: her second lover was killed in action during a campaign in Caria in 428/427.
This is all we know. Although the philosopher Aeschines, a pupil of Socrates, wrote a dialogue that was titled Aspasia (now lost), no author has ever written about Aspasia herself. If she is mentioned, it's because she was the wife of Pericles. She is in fact a historical unperson.
Still, she is mentioned several times. In Athenian comedies, she is called a harlot and a brothel keeper and is supposed to have had great influence on her husband's policy. The playwright Duris presented her as responsible for the Athenian attack on Samos in 440, and in 425, Aristophanes parodied the prologue of Herodotus's Histories, suggesting that the Archidamian War had broken out because a group of Megarians had taken away two girls from Aspasia's brothel (quote).
Compared to the way Aristophanes portrayed Cleon, Euripides, and Socrates, the comedian is kind towards Aspasia. But that does not make these remarks reliable biographical information. They were meant to strike at Pericles, who, it is suggested, shared his lover with other men, something that was considered to be a stain on his honor. And a man without honor, it was believed, could not command an army or lead the city.
The remarks also tell something about the Athenian contempt for a metic woman who seems to have played a role in the cultural life of her adopted hometown. "Seems": although several sources portray Aspasia as a woman of great intellectual powers who "taught Pericles how to speak" (and was, therefore, a philosopher and an orator in her own right), this is again parody. Any Greek politician was believed to have learned the tricks of the trade from someone else; making Pericles the pupil of a woman was again a form of mud-slinging.
On the other hand, it is possible that the fact that Aristophanes did not go to great lengths to damage the reputation of Aspasia, is evidence that she was a respected lady. But this is just a hypothesis.
So we are left with a rather disappointing conclusion: nothing is certain about Aspasia. She was the lover of Pericles, and that is all we know.
Madeleine M. Henry, Prisoner of History. Aspasia of Miletus and Her Biograpical Tradition (1995)