There are different reasons this is done.

1. Promoting children rights campaigns.

2. bringing the element of innocence to the game

3. Fulfilling children's dream of meeting their favorite star

4. To make money off the games, it should be noted that parents sometimes are asked to pay to feature their kids.

5. Protection of players; this is also a means of protecting football players from fans violence. Sometimes we see object being thrown at footballers. The presence of small children with them could avoid this, especially when the players are very close to the fan.

In some occasions we see footballers have been seen with their mothers as escort, to mark mothers day. Ajax Amsterdam did this in a match to mark mothers day. Source: Quora.com