A ba'al teshuvah is someone who has chosen to live a more religious Jewish life. BTs for short, they are often contrasted with FFBs (frum from birth), people who were brought up religious. Though existing in traditional Jewish literature for centuries, the word has become widespread over the past 40 years with the striking return to religious observance that has taken place over that time.
It can be used as an adjective, ba'al teshuvah-ish, meaning behaviour characteristic of ba'alei teshuvah, eg great zeal for religious observance combined with a certain lack of the knowledge that underpins it.
The phrase may seem to be a misnomer. Ba'al means owner or master, and teshuvah, which is often translated as "repentance", really means "return" from the verb lashuv. This sounds as if the ba'al teshuvah is going back to somewhere he was before, whereas most were never previously observant.
Mystics such as Rabbi Abraham Isaac Kook explain that the path of teshuvah is a journey towards the Divine Source of all existence from which which everything emanates. In this sense, it is a return.
In some parts of the observant world, ba'alei teshuvah are of somewhat lower standing than those fortunate enough to grow up religious. This distinction is not supported by the majority of traditional sources that I'm aware of.
The Talmud (Berachot 34b) writes that "even the completely righteous cannot stand in the place of ba'alei teshuvah." Commentators explain that one who was made the immense spiritual effort required to change his or her life has, by the power of that choice, achieved more than one who was religious all along.