Put very simply, being an active parent means being there for your child and with your child. Active parenting starts from the moment your child is born. Don't forget that fathers can and should have an active part in baby care. Most of us have been socialized to let mothers take the lead in dealing with babies and in most cases, moms are home with baby gaining parenting experience in the first months, while dads are out at work. Fathers may feel a lack of self-confidence, or even that they don't have the right to "interfere" when it comes to calming a crying infant, or feeding and changing their child. Mothers may add to that feeling when they quickly take over Dad's attempts to change a diaper; even more so when they criticize the father's way of doing things. In the best situation, moms and dads will share in both the "chores" of child rearing and the joyous times of playing and learning together.
As your children grow, being an active parent means being involved in your child's life as much as possible. Most of us are not stay-at-home parents, but there should still be a good few hours in the day when at least one parent can spend quality time with the kids. The active parent doesn't only relate directly to the child, however, but should also take the time to check in with teachers, coaches and parents of friends.
As children reach adolescence, they may want less parental involvement in their lives; it's natural and it's healthy, but it shouldn't stop you from being an active parent. Don't leave your involvement at the level of "I'm here if you want me." Make sure to be proactive in talking to your teens, and show them that you care what they think. Get to know your child and find things that you can enjoy doing together. Being a parent isn't easy, but it's not easy to grow up either. Help each other out and you'll both be the better for it.