Repentance can be a slightly confusing term, because we have very different words that translate to it. The Hebrew term used in the Old Testament, nicham, means "to feel sorrow," which makes the somewhat confusing phrase "the Lord repented of what he had done," seen various times in the OT, make a lot more sense.
The Greek metanoia used in the New Testament, on the other hand, does not mean contrition; it means "to change one's mind." And when John the Baptist was asked about his teachings of repentance, he made it clear that, as the mind drives our decisions, true repentance involves changing not only our thoughts, but our behavior:
8 Bring forth therefore fruits worthy of repentance, and begin not to
say within yourselves, We have Abraham to our father: for I say unto
you, That God is able of these stones to raise up children unto
9 And now also the axe is laid unto the root of the trees: every tree
therefore which bringeth not forth good fruit is hewn down, and cast
into the fire.
10 And the people asked him, saying, What shall we do then?
11 He answereth and saith unto them, He that hath two coats, let him
impart to him that hath none; and he that hath meat, let him do
12 Then came also publicans to be baptized, and said unto him, Master,
what shall we do?
13 And he said unto them, Exact no more than that which is appointed
14 And the soldiers likewise demanded of him, saying, And what shall
we do? And he said unto them, Do violence to no man, neither accuse
any falsely; and be content with your wages.
So true repentance does not simply require asking for forgiveness, or even "truly meaning it," but actually turning away from the sin. For how long? For the rest of your life, of course; if you only stop doing something for a short time and then go back to it, you haven't really turned away from it.