To involve means to connect. When you get involved in the Spanish Club, you attend meetings and events. If doing math well is involved in understanding advanced chemistry, that means it's a necessary part of it.
When someone is very involved, it means they are engaged or connected to a lot of activities. When someone is self-involved, all they connect with is him or herself. If getting ice cream involves walking a mile to the ice cream shop, the exercise offsets the indulgence. When no exercise is involved, it's less healthy.