Looks like the work of aphids. They secrete a sticky substance called honeydew (it's their poo). The 'honeydew' goes moldy after a while.

It looks like woolly aphids, which also secrete honeydew, like Bathgate says, but secrete a waxy fuzz, in addition. The fuzz helps protect them from aphid predators, but also may repel the more common insecticides. Spraying with soapy water usually helps with them, as long as the infestation isn't too advanced. When the population gets high, however, they will also colonize the roots, which makes control much more difficult.

Looks like woolly aphid to me too... if your apple tree isn't that large, and the infestation isn't too widespread, you can scrub them off with a brush, although I used a jeycloth lightly moistened with methylated spirits last time. Just don't get the meths on the foliage... wipe over with a damp cloth afterwards. Other advice below

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