Republicans tend to dominate in Texas, because Texans are historically conservative. They like small government, fewer taxes, and they want the government to legislate morality (anti-abortion, gay marriage, etc) so all of these things make the Republican party attractive. They also have strong oil interests, and the Republican party is more business-friendly. Democrats are not likely to have a strong hold there soon, with the exception of Texas's strong Hispanic population.
If you look at the platforms for both parties they say almost the same thing on some issues. In today's world of politics it is hard to determine what each party really believes. They say all the right things and then do whatever they want.
In general, Texas is a socially and politically conservative state that consistently votes for Republicans at the national and statewide level. Politics within Texas, however, are a bit more complex.
There are liberal islands of support for the Democrats scattered across the state and in the southern third of Texas, most notably in San Antonio, Austin, and the border region. A large Latino population, some native Tejanos, some recent immigrants, tend to support Democrats, and immigration is their central issue. They want a path to citizenship for undocumented workers currently living here. They supported the health care reform movement, and like most people in the US, economic hardship is their principle issue this election cycle.
Republicans, on the other hand, the overwhelming majority in the rest of the state and especially in Dallas, Houston and Midland, along with the Panhandle, are on the opposite side of the immigration issue, favor stronger border security, oppose most initiatives of President Obama, including health care reform, the stimulus package and the national debt, among others. They share liberals' concern about the economy, they simply differ in how to fix it. There is considerable support among Republicans for the Tea Party movement.
Republicans generally stand for less government, fiscal responsibility, are conservative, oppose activism of any kind, but also believe in many social causes are immoral and against the US Constitution such as gay marriage and abortion. The Democratic Party is basically against what the Republicans believe in,