Whether children are pushed or they are propelling themselves, kids use all their muscles to hold on, balance and coordinate their body movements with the rhythm of the swing. Swinging ahead and pulling back helps work the quadriceps and the hamstrings and both motions build strength in the arms, and build endurance in knee and hip joints. Balancing involves abdominal muscles, upper back, shoulders and neck.
Besides the physical workout, their brains get a workout as well as they see the environment from new angles and start to understand spatial learning of up and down and back and forth. Here’s more on how swing sets help the body and mind: http://www2.scholastic.com/browse/article.jsp?id=3746076