In Texas, judges are selected through direct, partisan elections. That means that they run for office as Republicans or Democrats and are elected by the public as a whole. They are selected in exactly the same way as members of the legislature, in other words.
The major pro of this system is that it makes judges more accountable to voters. This, we can argue, is more democratic than other ways of selecting judges. The people get to examine the candidates and choose the ones they want. This is the essence of democracy, at least from one point of view.
However, there are many criticisms of this manner of selecting judges. First, it causes judges to make decisions that will please the voters, not decisions that are in accordance with the law. Judges are supposed to follow the law, not the opinions of voters. Second, the system arguably makes judges less independent. Because they have to run for reelection, they need to have money. This means they have to solicit donations from various sources. This can make them less independent as they seek to please groups that have money to donate to them. Finally, it is possible that the quality of judges is lower because they are selected based on their ability to appeal to the public, not on their legal qualifications.