What most Americans have forgotten is that Texas was not only a part of Mexico up until the 1830s, but that the Lone Star State was actually the Lone Star Republic, an independent nation, for nine years, from 1836 - 45. This fact, and the way in which that nation came into being, sets Texas apart from the rest of the Union in a very significant way.
Texans are proud of their history of independence in both the political and social sense, and this is one reason why the Texan flag (the same flag as the independent country, incidentally) is often displayed so frequently and prominently on homes and bumper stickers. The phrase "Don't Mess With Texas", while used as a punchline and an expression of toughness, has its cultural roots in the Texas Revolution in the 1830s and the idea that Texans are indomitable.
Texas is one of our largest states, and has an economy equivalent to the size of a small country. It is rich in oil and farmland, and a frontier culture arose around both. This is also one reason why so many Texans are gun owners, and their laws on gun ownership are so permissive.