In order to help you to better understand your child's League of Legends games, I present you the game basics.
LoL is a video game developed by Riot Games in which 2 teams of 5 players compete against each other (the blue team on the left and the red one on the right).
Each player must select a champion from over hundred champions. This very strategic stage is called the draft phase.
The main game objective is very simple, just destroy the opponent's Nexus to win the game. To get to the Nexus, players can take 3 paths : the top lane, the middle lane and the bottom lane. On each of these lanes, protective turrets and an inhibitor are present. Players must destroy this protective equipment, on at least one lane, in order to reach the Nexus. To help them, small units (minions) advance at regular intervals along the 3 lanes. The minions will attack anything in their path that is not part of their team.
There are five positions in a LoL team. It's important to know them so that you know which position your child and each of his/her teammates are playing in.
Generally, the Top will play on the top lane, the Mid will be on the mid lane, the AD Carry and the support will be on the bot lane and finally the jungler will play mostly in the other parts of the map outside the lanes (the jungle).
During the game, each champion will try to become more and more powerful by leveling up with experience and collecting gold to buy items. A champion can gain experience and gold mainly by killing minions, jungle monsters, enemy champions and destroying structures.
In the jungle, there are some very important monsters and players will regularly fight each other to get them.
Baron Nashor is the most powerful monster in the jungle. He gives the team that kills him powerful temporary upgrades, very useful for destroying structures and advancing to the enemy Nexus.
Drakes grant unique bonuses based on the element of the drake eliminated. There are four Elemental drakes and one Elder dragon.
The attached map illustrates what I have just explained with zoom in on the important points. You can also find this information a little more detailed on the LoL website.