Spectres are a subclass of Ghosts that have become too unstable. Damaging or disrupting a ghost and breaking its pattern causes it to spiral out of control and leaves it unable to maintain continuity. When it goes it tends to drag a few people with it before it’s spent. Normally they're only seen around an area with another presence at work or if it’s tightly bound to something and its focus is destroyed.
Spectres can't be reliably bound since they are too unstable, but they can be used as a sort of agony bomb. The Shepard managed to do this by forcing other ghosts into a single one and then causing it to rupture as a weapon. Doing this, however, wiped out the spectre.