Like the U.S. Congress and the legislatures of all states but Nebraska the state lawmaking institution in Texas has two houses, an upper house (the Senate) and a lower house (the House of Representatives).
This bicameralism- the division of the legislature into two chambers - is part of a long tradition in Anglo-American and Western political history. In the United States this tradition was rationalized by the framers of the Constitution as a way of deliberately weakening the Congress, the branch of government most directly influenced by popular pressure. By splitting the popular branch in two, goes the argument, you make it more difficult for that branch to coordinate efforts for any particular legislative agenda.
The bicameral Congress was also the solution to the stalemate between the populous states and the relatively sparsely populated states. The latter feared that a single legislative chamber whose seats were to be apportioned by population would put them at a perpetual disadvantage on key issues. The famous Connecticut Compromise broke the impasse by proposing a second chamber in which each state would get two seats.
On the state level, the seats in both houses of the legislature are apportioned by population. Nevertheless, the bicameral state legislature means that any bill that is introduced must twice wend its way through a complex process of review, amendment, and approval. This extends considerably the time it takes to pass a law, and it introduces many more opportunities to derail a bill. The net effect is to restrict the overall volume of successful legislation.