These little tykes pop up mostly in "Burnt Norton," frolicking in a bunch of fallen leaves, but the speaker also comes back to them in the latter parts of the poem, too, especially the final flurry of "Little Gidding" (875).
All in all, children have a pretty conventional meaning in this poem. They represent the innocence of play and the ability to totally live inside the moment. Children are generally great because they're less invested in posturing than adults are. Children don't care about the past because there isn't much of it to care about (because they're young). They also aren't worried about the future the way adults are because they prefer to enjoy themselves in the moment. You could say that this is because children don't have responsibilities to provide for themselves, but the speaker would prefer that we forget that for the time being.
Lines 42-43: Here, the children are a basic symbol of innocence and happiness.
Lines 174-175: At the end of "Burnt Norton," the speaker revisits the image of children playing, which continues to symbolize our human ability to live totally in the present moment, sadly something we lose as we age.
Lines 875-876: In these closing moment of "Four Quartets," the speaker returns to these children one last time as he tries to gather his motifs from all four quartets and make one last gambit to get us on board with the idea of becoming more childlike ourselves and learning to enjoy the world for what it is.