Caterpillars and webbing on my backyard apple tree
This is fall webworm. There are two generations and the spring one is usually unnoticed, but this year numbers are high. It doesn't usually do significant damage, except perhaps on a small tree, however in that case pruning out the nests removes so much of the tree that manually pulling it out would probably be better.
It's a native, so it's a great food source for birds.
In general, you can cut it out, or break it up and let the birds in. Or, you can manually pull it out and drop it in a bucket of soapy water to kill the larvae.
Here's directions: http://extension.umd.edu/hgic/fall-webworm-trees
No insecticide treatment is necessary.