This is a difficult question to answer, because many specific ideas come under the label of “theistic evolution.” It may at least be helpful to consider one particular question, whether the Earth was created in six 24-hour periods.
Augustine of Hippo, writing more than fourteen hundred years before Darwin, confesses that he does not understand the meaning of the days of creation, because what does it mean to have days before the Sun existed?
We see, indeed, that our ordinary days have no evening but by the
setting, and no morning but by the rising, of the sun; but the first
three days of all were passed without sun, since it is reported to
have been made on the fourth day. And first of all, indeed, light was
made by the word of God, and God, we read, separated it from the
darkness, and called the light Day, and the darkness Night; but what
kind of light that was, and by what periodic movement it made evening
and morning, is beyond the reach of our senses; neither can we
understand how it was, and yet must unhesitatingly believe it. (City of God I.7)
I imagine is that every other issue would motivate someone to accept theistic evolution follows the same reasoning. One reads the Bible and concludes that the literal meaning surely cannot be the intended meaning—and perhaps we cannot understand the intended meaning, or perhaps we can make guesses.
(This is, incidentally, the way almost all communication works. If I say, “My supervisor is a real monster,” you are not confused, because you know that I don't believe in monsters, so you can safely infer that my meaning is metaphorical.)