We all (not just children) play by challenging ourselves. "Why do you want to climb Mt. Everest?" "Because it's there," said George Mallory. And we all do the same thing, though usually on a smaller scale: running a marathon, learning a computer language, fixing a car, building a deck, sewing a prom dress.
In the life of a young child, challenge is everything--it's how they are able to do new things each day. Some kids are maniacs for it, and will keep trying something difficult until they succeed or get hurt (or both). Others are more laid back, but still enjoy a quiet challenge; puzzles, games, and the like. A friend of mine likes to take a stopwatch to a playground and have his kids do something--"go climb over that and run back to me"--and then they see if they can do it faster the next time. He says that it doesn't take more than a few minutes for the other kids on the playground to notice what is going on and then they ALL want in on it--who is the fastest, strongest, most agile, etc. The man with the stopwatch is the most popular guy on the playground.
Which means that a parent who recognizes that challenges are vital to growth, and provides many opportunities for kids to stretch, is giving them what they need. Russian psychologist Lev Vygotsky formulated a theory of the Zone of Proximal Development, which has influenced my homeschool-mothering. He stated that each person grows and develops at different rates, but has distinct "tasks" that he is capable of mastering if he puts forth effort. For example, after I have taken my first ski lesson I'm not ready for the crazy-daring mountainside. The bunny hill is now in my Zone of Proximal Development though.
Each person has a ZPD for math, for language, for reading, driving, sewing, woodworking, computers, etc. Whether or not you proceed to learn that next step depends on your interest and/or need of the skill. So how do you know where your child's ZPDs are? A preschooler may be able to put on shoes that fasten with velcro, but is not yet able to tie his shoes. If he eagerly watches you tie shoes and attempts it on his own, you can be pretty sure he's ready for some lessons and encouragement. Just because he can already do velcro shoes, and lace-up shoes are next, doesn't mean he's ready to move on--it may not be in his ZPD yet, considering the manual dexterity and memory skills necessary.
So the goal can be really big, but if he is able to break it down into small steps that fit within his ZPD, the child will want to embrace the challenge as a form of play.