This is an individual beech blight aphid.

What is the white stuff sticking out of its butt? According to Insect Identification - Beech Blight Aphid (Grylloprociphilus imbricator)
This hairy substance is actually made of strings of wax that the aphid secretes onto itself. The texture of the wax is thought to be unappealing to beetles and wasps that might eat it. It is also an efficient way of reducing the loss of water by providing a hydro-phobic barrier that prevents evaporation.

Like other aphids, they use their mouth parts to drain their host plant of its juices. They then produce a sticky, sweet substance called honeydew from the plant juices once they eliminate it. Honeydew is a sweet, attractive food source for ants and, therefore, it is likely to find ants in the vicinity of aphids in order to harvest the sap-like excretion.

Are they bad for the trees?
The aphids do not usually damage the trees, but some die-back may be seen on intensely colonized branches.
- from Preservation Parks - Delaware County - Let's Boogie Woogie!

What affect do the beech blight aphids have on humans and other animals? One source claims
The nymphs are highly aggressive against predators and will mass-attack using their piercing-sucking mouthparts to inflict serious damage to their assailants.
- from Buckeye Yard & Garden onLine - Boogie-Woogie Aphids are Still Dancing

But seriously, just how bad is the sting of the beech blight aphid to a person?
...humans could detect the "stings" of the larvae when handling them, but their 'stings' only caused minor irritation.
- from Influential Points - Grylloprociphilus imbricator

The best place to find beech blight aphids is on small branches and the underside of leaves of American beech trees usually starting in mid-July.
- from "Preservation Parks - Delaware County - Let's Boogie Woogie!"

We only found a single tree containing them...but believe you me, there were a LOT!

Norma found that if you blow on or otherwise disturb the beech blight aphids, they will sway from side to side. This is why they are nicknamed the "boogie-woogie aphid." Here's a video I made that starts out at regular speed and then slows down. Had the aphids twerked in unison, I would have added music. Click on the image to start the video.

I mentioned that the massive quantity of aphids created its own little ecosystem. So what else did we find?

In the below snapshot, the thing on the left is a harvester butterfly caterpillar (Feniseca tarquinius), the only strictly meat-eating butterfly caterpillar found in the U.S. These are known to feed on beech blight aphids.
- from Influential Points - Grylloprociphilus imbricator

Beech blights weren't the only aphids living on this tree. I also saw giant bark aphids (Longistigma caryae).
- from Maryland Biodiversity Project - Giant Bark Aphid

On several branches of the beech tree hosting the beech blight aphids, we found Scolias spongiosa,
...commonly called beech blight sooty mold. It is also sometimes called the beech blight aphid poop eater because of its food supply and obligate relationship to the aphid; the fungus only grows on honeydew produced by the beech blight aphid. The fungus starts out behaving like most sooty mold fungi; it grows as a dense, black, "fuzzy" mat on top of the honeydew. Over time, the mat thickens into a brownish, furry mass. Then the fungus progresses into a growth phase that is unlike most sooty molds; it produces a spongy, golden-yellow heap that may rise 1 - 2" or more above the leaf or twig surface. The odd looking fungal growths look like nothing else that would commonly be associated with aphids or honeydew. It may also attract yellowjackets and baldfaced hornets in search of a sugary meal. - from Buckeye Yard & Garden onLine - Boogie-Woogie Aphid Takes Center Stage

Indeed, we did find numerous yellowjackets or hornets in the area.

Scorias spongiosa is a specialist and grows exclusively on the honeydew formed by colonies of the beech blight aphid. This aphid is found only on one host plant, the American beech tree, Fagus grandifolia, where it congregates on branches and twigs, creating copious amounts of honeydew that drip onto vegetation below. The large quantity of honeydew enables this fungus to grow to a large size, much bigger than other sooty mould fungi, which produce only a thin black layer on the surface of leaves.
- from Wikipedia - Scorias spongiosa

I felt truly blessed that day to have witnessed one of nature's great spectacles.