As with so many other words and concepts, we might all have a different understanding of what a sport is. On this site, when I talk about sports, I define the word broadly. I think it can include almost any kind of physical activity.
What is a sport? An activity that works your heart and lungs, raising your heart rate and improving cardiovascular endurance. This could mean playing soccer or basketball with a team, or running or swimming on your own. It could also mean dancing, hiking, or even playing tag or another active party game.
What is a sport? An activity that strengthens your muscles and bones. Don't just think weight-lifting and push-ups; think yoga, gymnastics, running and walking. All are weight-bearing exercises that are beneficial for bones.
Must sports be competitive? I don't believe competition against others is required for an activity to be considered a sport. We can still derive all of the fitness benefits of physical activity without keeping score or being judged. For some people, competition (whether against an opponent, or our own past performance) is motivating—maybe even the only motivator that really works. Others may respond to different motivators: a love of the game, a love of the outdoors, a love of teammates, a need to try something new and different.
There are lists of sports that are recognized by the National Collegiate Athletic Association (NCAA) and the International Olympic Committee (IOC). But not only do these leave out some popular athletic pursuits (for example, baseball, inline skating, golf, karate, lacrosse, rugby and squash are not Olympic sports), they can change often. So-called "extreme sports" like snowboarding and mountain biking are only recent additions to the Olympic Games, but their fans enjoyed them for years without the Olympic seal of approval.
Does the answer to this question really matter? Not really, unless it stands in the way of you or your child finding the kind of physical activity you'll enjoy and stick with. If hiking is your thing, don't waste your time trying in vain to enjoy volleyball. If your child loves to tap dance, don't pressure her to take up tennis. It's far more important that she, and you, move your bodies as often as you possibly can, while protecting yourself from injury as best you can. When you do that? You're playing a sport, and you're an athlete—no matter what the dictionary, the NCAA, or the IOC says about it.