Miriam was Aaron and Moses's older sister. According to some sources, she was seven years older than Moses, but other sources seem to indicate that she was older than that. Some sources indicate that Miriam was Puah, one of the midwives who rescued Hebrew babies from Pharaoh's edict against them (Ex. 1:15-19).
Miriam was a prophetess in her own right (Ex. 15:20), the first woman described that way in scripture (although Sarah is also considered to be a prophetess, that word is not applied to her in scripture). According to tradition, she prophesied before Moses's birth that her parents would give birth to the person who would bring about their people's redemption.
Miriam waited among the bulrushes while Moses's ark was in the river, watching over him to make sure he was all right (Ex. 2:4). When the Pharaoh's daughter drew Moses out of the water, Miriam arranged for their mother, Yocheved, to nurse Moses and raise him until he was weaned (Ex. 2:7-9).
Miriam led the women of Israel in a song and dance of celebration after the Pharaoh's men were drowned in the sea (Ex. 15:20-21). She is said to be the ancestress of other creative geniuses in Israel's history: Bezalel, the architect of the mishkan (the portable sanctuary used in the desert) (Ex. 31:1-3) and King David.
According to tradition, because of Miriam's righteousness, a well followed the people through the desert throughout their wanderings, and that well remained with them until the day of Miriam's death.
Like her brothers, Miriam was not perfect. She led her brother Aaron to speak against Moses over a matter involving a Cushite woman he had married (Zipporah, or possibly a second wife) (Num. 12:1). They also objected to his leadership, noting that he had no monopoly on Divine Communication (Num12:2). For this, Miriam was punished with tzaaras (an affliction generally translated as leprosy) (Num. 12:10). However, Aaron pled on her behalf, and she was cured (Num. 12:11).
Like her brothers, Miriam died in the desert before the people reached the Promised Land (Num. 20:1).
Sources: Judaism 101