The term "theistic evolution" is used in contrast to the atheistic idea of evolution. It means evolution set in motion by God or under the direction of God, and seems appropriate for a believer who admits some truth to evolutionary science.
But I do not like the phrase because it is a confusing redundancy. Think about it. If you are a believer, it is already implied that you see all biological and physical processes as created and held in existence by God. You do not need "theistic" in front of biological terms. Who speaks of theistic reproduction? Or theistic gestation, theistic meiosis, or theistic menstruation? Plus, to qualify a biological process as "theistic" implies that the opposite is possible, that God may not be involved in creating certain laws of nature.
Just leave the unnecessary adjective out and treat evolutionary science as a biological and physical science. Refuse to treat it as anything else. Judge it on its scientific merits or lack thereof.
Such realism clarifies a point: truth about the physical realm is objective. Whatever is scientifically true, ultimately, is theologically true. If our current knowledge seems contradictory, it is because we are creatures who rely on sensory data to form abstractions and because we are not in possession of all knowledge. That fact of our existence is why we need the scientific method. Humans do stare out at the landscape and mentally see all the knowledge that they can grasp. We search systematically, one step at a time, constantly piecing together our best collective efforts to grasp the bigger picture. Within that quest, the interpretations of scientific findings are also, at times, quite subjective as well because each scientist brings his or her own starting assumptions to the table. Science and theology are, by necessity, complementary searches. We do not need to put boundaries around God or use science to shore up our faith.
I have come to view science somewhat like (majorly ramped up) cooking and the faith and science discussion like a group of people gathered around the kitchen table to appreciate the fruits of those labors. Both science and cooking are human endeavors to discover properties of matter and manipulate those laws to produce something, be it polyelectrolytes or pepperoni pizza. Believers and non-believers can cook in the same kitchen and sit at the same table. Sure, the grateful believer asks the Lord to bless his meal, but the atheist can observe and partake of the object of gratitude too, even if he or she does not say any prayers or offer any thanks. No one calls the process by which food gets on the table theistic gardening or theistic baking.
Richard Dawkins called the term "theistic evolution" an attempt to "smuggle God in by the back door," and he was right. God does not need us to do that. We can be confident that God, who became Incarnate, makes Himself known through His creation. When we gather to assess and critique evolutionary science, the believers will praise God for his handiwork and the atheists will do whatever they do. To grasp this confidence and clarity is to grasp why science does not draw a rational person away from religion. In fact, science, like a good meal shared among friends, can even draw a searching mind closer to our Maker.