Involvement is the act of participating in something. Even if you do nothing but drive the getaway car, you will be held to account for your involvement in a crime.
Involvement is useful because it is not specific. If, over the course of many years, you play and then coach football, you might refer to the time of your involvement in the sport. If you are engaged in a love affair, you might say, without going into too much detail, that you and your lover are involved and refer to the affair as your involvement.