Sometimes, due to young children being not as strong, they might release the flush lever / button to quickly or not activate the flush lever / button all the way. That causes the tank of water to not completely release, and thus, making the toilet to not flush fully or not flush at all.

Other times, it's simply clogged. Speaking of clogged toilets, somehow, my older son used to often clog both our toilet at home, and also friends' and family's toilets. His toilet clogging trophies include my parents', father in law's, both of my 2 sister in laws', 2 of my cousins', 2 of wife's friends', 1 of my friends', twice when we were traveling in the hotel, and of course, numerous times at home. One time, our toilet got clogged so bad, the plunger wasn't able to solve the problem, and I went to Home Depot to buy a toilet auger to take care of it. That was also the first time I learned about the toilet auger.