Ms. Marvel was originally Carol Danvers, just a regular human working at NASA where she happened to meet one Dr. Phillip Lawson (we know him as the Kree super hero called Captain Marvel). A romance blossomed between them after he saves her life and after hearing of said romance, a Kree enemy (Yon-Rogg) kidnaps Carol to draw Captain Marvel into a trap. During the fight, the Captain shields her from a powerful, and forbidden, Kree machine known as the Psyche-Magnitron.
The machine (essentially) pushes radiation through Captain Marvel into her, which effectively mixes her human DNA with that of the Kree. The process was influenced by her wanting to be Marvel's equal, instead of the helpless girl he kept saving, as well as her dreams of flight and having super powers. As a result, the encounter leaves her with her first set of abilities: super-strength, durability, enhanced fighting skills on par with the Kree Warriors, a 'danger' sense, and flight. She adopted the name Ms. Marvel then.
Later she was in a battle with Rogue that left her powerless, eventually got herself kidnapped by more aliens (the Brood race this time), and their experimenting left her with much stronger powers than before. She changed her name to Binary for some time, but she still retained a form of flight and eventually her original, albeit enhanced, powers came back to her, where after she returned to the Avengers.