This is just a new activity for you all to try! You can start doing it with your baby when he has adequate head control, to be able to move his head to get comfortable. When you see your baby looking at and lifting his legs, this is definitely a good time to try this exercise with him!
I got my baby girl a tummy time mat recently, and it came with a small arc shaped cushion. I use it now for something completely different too! I have used this exercise with many children in therapy, and both the babies and moms love it! Its something we do for body scheme development, as well as coordination, mid-line crossing, rolling back to tummy and also (but mostly) tummy muscle strengthening!
An activity like this is also very good for babies with low birth weight or premature babies, as they weren't able to gain as much sensory input through the feet when kicking in-utero, since they had more space than term or bigger babies. This helps to learn about the feet - something that advances them when learning to walk or stand!
You place baby on his/her back with the small cushion/blanket/towel under just the bum, stopping at the hips. Make sure it lifts the bum cheeks up but doesn't cause strain on the neck by making too high of a head/trunk angle. It is basically playing whilst lying on the back, but by raising the hips we created more of a flexed position, encouraging leg kicking, and working tummy muscles. Babies who just lie flat on their backs find it harder to bring their legs into the air, so this gives them a view of their feet to motivate them to do this - and makes it easier to move the legs up and down!
What this should help baby do is bring his legs up first straight out and then after some time bent and close to the body. If you put yourself in this position, move your legs up and down and feel just how much your tummy muscles are working! Encourage him to look at and touch his knees and feet, with opposite hands to feet and also the same side foot to hand. He probably wont be able to get a firm grasp on the foot yet but now he's just learning that there is a foot there to begin with. You can also take both feet together and lift them up to touch his face but don't hold this position for long. Get baby to look at his feet when he is barefoot, and you can also put brightly colored socks on his feet to look at. Some socks have small bulging animals and rattles too, these are also good for this type of exercise!
You can also hold his body flat, bend his legs at the knees and stretch the hips by moving the legs from side to side (bent legs only with body flat on floor). This stretches the tummy rotator muscles involved in rolling and the hip joints!
Just a tip for moms with babies who spit up and reflux a lot - wait half an hour to an hour after feeds to do this activity.
My baby girl has a little bell toy hanging from her activity gym that she kicks while in this position and she loves it. Happy playing all!