It's an elective term rather than lifetime appointment, so there's hope of getting rid of Texas Supreme Court justices. The Texas Supreme court handles civil matters only, a separate court handling criminal cases.
The Chief Justice and the associate justices are elected to staggered six-year terms in state-wide partisan elections. When a vacancy arises the Governor of Texas may appoint Justices, subject to Senate confirmation, to serve out the remainder of an unexpired term until the next general election. As of 2010, six of the current Justices, a majority, were originally appointed by Governor Rick Perry. The current Justices, like all the Judges of the Texas Court of Criminal Appeals, are all Republican.
The place numbers have no special meaning as all justices are elected state-wide, except that the Chief Justice position is considered "Place 1".