According to the Tucson Chamber of Commerce, the name Tucson is derived from the Indian word, 'Chuk-son,' meaning village of the dark spring at the foot of the mountains.
The city was established in 1775 by Spanish soldiers as a walled presidio - the Presidio of San Augustin de Tucson. Tucson became a part of Mexico in 1821 when Mexico won its independence from Spain, and in 1854 became a part of the United States as part of the Gadsden Purchase.
Today, Tucson is still referred to as "The Old Pueblo."
Just a note: Common misspellings of the name of the city include Tuscon and Tuson. Tucson is pronounced: too-sahn. The City of Tucson's website also allows for the pronunciation of Tucson as: too-sahn. A person who lives in Tucson is called a Tucsonan (too-sohn-en). A person who lives in Arizona is an Arizonan (a-riz-oh-nen).
Oh, and one more thing: Ohio is the only other state I could find that has a city named Tucson.