This periodic readjustment is necessary to give all of the districts approximately the same number of people. If we didn't readjust the districts periodically, some districts would eventually have many more people than others, giving voters in less populated districts more influence in a particular legislative chamber or board. Also, as Texas has gained seats in the U.S. House of Representatives in each national census in recent decades, it has needed to reapportion these seats within the state. After the 2000 census, for instance, Texas gained two additional seats in the U.S. House.
The Texas Constitution of 1876 required that the Legislature pass a redistricting plan during the first session after the publication of the decennial national census of the population. However, the Legislature sometimes did not follow through on this obligation.  This resulted in the under-representation of the people in those districts where population grew faster than the rest of the state. The failure to redistrict favored the rural areas at the expense of Texas's growing urban centers. The latter's faster population growth meant they deserved additional seats in the state Legislature and the U.S. Congress.
Because of the great imbalance in representation that had developed over the decades, an amendment was adopted in 1948 that gave the Legislature extra incentive to carry out their obligations as specified under the original Constitution. Under this amendment, if in the first legislative session after the publication of the decennial census of the population a redistricting plan was not adopted, the responsibility passed to the Legislative Redistricting Board (LRB). The LRB is composed of the Lieutenant Governor, Speaker of the House, Attorney General, Comptroller of Public Accounts, and Commissioner of the General Land Office. The prospect of the LRB determining district boundaries represented a significant incentive to the Legislature to seriously engage its redistricting obligation, as a LRB-authored plan would diminish significantly lawmakers' control over their own reelection fates.
6 See the Texas Secretary of State's website at http://www.sos.state.tx.us/elections/voter/faqcensus.shtml for Frequently Asked Questions regarding the census and redistricting
7 Brown, et al. Practicing Texas Politics, 11th Edition (2001), p. 222