That's when it achieved 'official' statehood. Before that it was a sovereign state that had broken away from Mexico. Independence from Mexico was a first step that eventually led to full partnership in the union. So astrologically you might say that March 2 Independence was the day of conception and Dec. 29th was the date of birth as a full state entity in its current form.
From Wikipedia:
The Republic of Texas was a sovereign state in North America between the United States and Mexico that existed from 1836 to 1845. Formed as a break-away republic from Mexico by the Texas Revolution, the nation claimed borders that encompassed an area that included all of the present U.S. state of Texas, as well as parts of present-day New Mexico, Oklahoma, Kansas, Colorado, and Wyoming based upon the Treaties of Velasco between the newly created Texas republic and Mexico. The eastern boundary with the United States was defined by the Adams-Onís Treaty between the United States and Spain, in 1819. Its southern and western-most boundary with Mexico was under dispute throughout the existence of the Republic, with Texas claiming that the boundary was the Rio Grande, and Mexico claiming the Nueces River as the boundary. This dispute would later become a trigger for the Mexican–American War, after the annexation of Texas.
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On February 28, 1845, the U.S. Congress passed a bill that would authorize the United States to annex the Republic of Texas. On March 1 U.S. President John Tyler signed the bill. The legislation set the date for annexation for December 29 of the same year. Faced with imminent American annexation of Texas, Charles Elliot and Alphonse de Saliny, the British and French ministers to Texas, were dispatched to Mexico City by their governments. Meeting together with Mexico's foreign secretary, they signed a "Diplomatic Act" which offered Mexican recognization of Texas independence, with boundaries that would be determined with French and English mediation. Texas President Jones forwarded both offers to a specially elected convention meeting at Austin, and the American proposal was accepted with only one dissenting vote. The Mexican proposal was never put to a vote. Following the previous decree of President Jones, the proposal was then put to a national vote.
On October 13, 1845 a large majority of voters in the Republic approved both the American offer and the proposed constitution that specifically endorsed slavery and the slave trade. This constitution was later accepted by the U.S. Congress, making Texas a U.S. state on the same day annexation took effect, December 29, 1845 (therefore bypassing a territorial phase)<1>. One of the motivations for annexation (besides the primary one of desiring to be united with their perceived Anglo-American ethno-cultural brethren of the United States and their Anglo-American brethren of "the South" regional-cultural was that the Texas government had incurred huge debts which the United States agreed to assume upon annexation. In 1852, in return for this assumption of debt, a large portion of Texas-claimed territory, now parts of Colorado, Kansas, Oklahoma, New Mexico, and Wyoming, was ceded to the Federal government.
The annexation resolution has been the topic of some incorrect historical beliefs— one that remains is that the resolution granted Texas the explicit right to secede from the Union. This was a right argued by some to be implicitly held by all states at the time, up until the conclusion of the Civil War. The resolution did include two unique provisions: first, it said that up to four additional states could be created from Texas's territory, with the consent of the State of Texas. The resolution did not include any special exceptions to the provisions of the US Constitution regarding statehood. The right to create these possible new states was not "reserved" for Texas, as is sometimes stated. <2>. Second, Texas did not have to surrender its public lands to the federal government. While Texas did cede all territory outside of its current area to the federal government in 1850, it did not cede any public lands within its current boundaries. This means that generally, the only lands owned by the federal government within Texas have actually been purchased by the government. This also means that the state government has control over oil reserves which were later used to fund the state's public university system. In addition, the state's control over offshore oil reserves in Texas runs out to 3 leagues (10.357015 miles) rather than three miles (5 km) as with other states <3>.
http://en.wikipedia.org/wiki/Republic_of_Texas