What is an act of contrition? I did not ask, what is "the" Act of Contrition. What I mean by that is we need to understand the action of being contrite if we expect to understand the prayer that is called the Act of Contrition. There are a few different forms of the Act of Contrition; both traditional and modern (compare them and see which is more precise and reverent).
What does it mean to be "contrite"? When someone is contrite he recognizes the gravity of his faults and sins. He does not blame someone else for what he has done. He also is able to admit that his sins have wronged someone else, most especially God. A contrite person is one who truly desires to overcome his own sins and is willing to do the work necessary to accomplish that.
At the heart of the matter is the intent to change. The contrite person intends to change something in his life in order to avoid falling into the sins that were confessed in the confessional. If there is no real intention to change something in one's life (anything!), then there is definitely not any true contrition. Having the intent to change does not mean that you "promise" or make any guarantee to be sinless. It means that you do not plan on just going back to doing things the way that you did before which (you know) will just lead to you committing the same sins again.
This is why the Church has the prayer called the Act of Contrition. It summarizes those things mentioned above in a few simple words. It is important for us to learn what the action of contrition is like, so that we can recognize if we do not have true contrition. True contrition is essentially the same as penitence, so without it there is no true forgiveness.
Finally, I should make a comment about the practice (not sure where it began) of making up your own Act of Contrition. This is not exactly a horrible thing to do, but it not exactly a great idea either. Here is why: I cannot tell you how many times I have been in confession and heard someone say an act of contrition that he or she made up and I could not tell if there was a truly contrite heart behind it because it was so vague. Many of the "self-authored" acts of contrition amount to "Gee God, I'm sorry." Not much there to go with. Sadly, these are often made up right there in the confessional, so it ends up sounding like "God, um, I, uh, am sorry, and wanna, um, uh, just be good".
Yes, it is bad merely to recite a prayer that does not mean anything to you, but to recite a prayer you wrote that does not mean much is not a solution; nor is it any better if you shoot from the hip and miss the target. If you wish to speak extemporaneously in your act of contrition, then at the very least make sure that you express a clear and genuine penitence and that your words amount to more than "yeah, I probably shouldn't have done that."
I cannot say this enough: Go To Confession.