Tejano is the word for the culture and music of the Hispanic population of Texas, which has its heartland in the Rio Grande valley. Tejano culture has a 300 year lineage, and is unique because of the admixture of Mexican and Texan cultural elements over the course of that time.
Tejanos speak a unique dialect of Spanish, called Tex-Mex, or, more derisively, Spanglish, which consists of Spanish grammatical structures with many English loan words. Tejano cuisine is also distinct from that of Mexican, and is probably best characterized by more deep-frying and the use of flour for tortillas instead of the more traditional corn. Most "Mexican" restaurants in America serve Tex-Mex food, and many culinary ideas which started in Tejano cooking have since filtered back to Mexico, further confusing matters.
Tejano music is also quite unique, and very popular even among the Anglo population of Texas. It is a mixture of traditional elements of Mexican country ballads, waltz and polka forms brought to Texas by central European immigrants, the country-western music of the Scots-Irish Texans, and Mexican and American pop music.