It depends on the ages of the children to how you would explain it. They may not fully understand how species change over time so it may be a hard concept to grasp.
Maybe use the example of say a giraffe.
Giraffes need long necks to get to the leaves in high trees.
You could explain that maybe there were two families of giraffes in an area, one family with very long necks, the other with shorter necks.
The giraffes with short necks could not get to the leaves so were always hungry and gradually they all died.
The giraffes with long necks were able to get to the leaves, stay strong and healthy, and survive.
Because the giraffes that survived had long necks their children were more likely to have long necks and so that family of giraffes survived whereas the one with short necks died out.
Other things that can help animals survive over time is beak shape, colour, size, ability to survive heat or cold, and so on.