The rainbow symbolises a phantasmagorial space. Its semicircle tightens like a protective shield over the children. It gives room for their creative urges. The ascending bubbles refer to an arena or stage.
Talking about graphical aspects of the logo you can say that the concentrical coloured circels symbolise the center itself. In black and white version that issue becomes even more clearly than in the coloured version. Each of them has its special quality.