Probably sees them as a potential threat, a good few years ago i had a Rough legged buzzard land just yards from my front door on some land,the area was fenced of and within minutes the Buzzard was surrounded by Crows and Rooks all sitting on the fence making plenty of noise ,they certainly turned up in numbers and this was October outside breeding time ,it made a good spectacle but also surprised how quick and how many turned up to warn the bird off ...
They will mob all predator birds, I've seen it with Buzzards, Peregrines, Marsh Harriers and a Goshawk (turned and ran though when the Goshawk had enough!).
Competition as much as anything.
Our local pair of carrion crows seem to be on territory most of the year but attacks are mainly during the nesting season.
Any predator,including ravens, which flies over the crows territory will be met by both birds and harassed until it moves on. Buzzards are often attacked,possibly because they are slower than other raptors, but may be responsible for predating fledged crows (kites often predate fledged jackdaws). The buzzard and crow territories sometimes overlap.
I once watched a small flock of about 8 carrion crows attack and probably kill a recently fledged buzzard by forcing it into wet foliage again and again until it could no longer fly.
Regen
We used to have a herring gull problem at work. In the nesting season when the gulls came in en masse if we got bored with work we could watch the aerobatics outside - the gulls would hassle the crows, the crows would go and beat up the gulls, rewind and start all over again.
Crows, other corvids and some other birds will mob any bird (or other animal) they see as a potential threat. I think the perceived threat is generally toward their young. Buzzards, other birds of prey and gulls are all potential threats to young birds but the mobbing response extends, as Dennis has noted, to outside the breeding season.
A few weeks ago while out with the dog we flushed out a couple of young foxes. Almost immediately a groups of crow set off after them. I've also seen crows sitting around a fox just watching - keep your friends close but keep your enemies closer.
Dave