Wright's childhood was "nomadic", as his father would travel from a ministry position to another throughout the Central and Northeast United States until they finally settled down in Madison, Wisconsin in 1878. In 1887, he left Madison for Chicago to pursue an architecture career, working for two different firms before being hired by Adler and Sullivan. There he worked for six years.
In 1889, Wright got married and borrowed money through a contract from Sullivan to build his own home. He also began taking up independent residential commissions in his spare time. In 1893, Sullivan found out and charged Wright for breach of contract, resulting in Wright leaving the firm and setting up his own office.
His main goal was to create an indigenous American architecture, and over the next sixteen years, he set standards for what became known as the Prairie Style. "These houses reflected the long, low horizontal prairie on which they sat with low-pitched roofs, deep overhangs, no attics or basements, and generally long rows of casement windows that further emphasized the horizontal theme."
His most famous works are Falling Water (residential house) and the Guggenheim Museum in NYC:
While both serve very different purposes and reside in vastly different environments, Wright's approach and "organic architecture" style are obvious. His constant uses of "layering" gives his buildings an organic quality---allowing Falling Water to perfectly complement its setting, as if the house should have been there the entire time, and bestowing the Guggenheim Museum with an eerie "concrete jungle" feel as it brings art into the urban landscape. And that is what I find the most compelling about his work. Separately, I don't like the techniques he uses (who would want small windows in their house?), but when Wright brings them all together and unites it with the environment, it remarkably works out spectacularly.
As a last note, I also want to include some of his glass work. They were often in the residences he designed and these stained glass windows really helped make his designs iconic: