|Horse chestnut scale|
The females shown in the picture breed by a process of parthenogenesis - don't mate with males- so that a close look shows them looking pretty bored. The white 'skirt' is where the eggs are, about 2,000 per scale, and mother dies when she's finished laying. The corpse remains attached to the egg sac, giving some protection to the contents but presumably not much satisfaction to mum.
All scale are sap-suckers but usually the host plant is so large that there is little real damage apart from aesthetically. This is good because controlling the problem on a large tree, short of burning it to the ground, is next to impossible. This brings to mind the old Benny Hill sketch where he pulverises a tomato plant with a large lump hammer:
"Don't do the tomato much good", he says with a cheeky smile and what I take to be a west country accent, "but it gets rid of the greenfly". For more about horse chestnut problems go to this.
The main thing my researches have come up with is the fact that no one seems to know a lot about the problem so, if you're really worried about it, try growing spuds.