When you mount a camera on a tripod all the forces are translated to that point.
For "small" or "light" lenses the centre of mass is somewhere in the camera body or near to it.
When the lens is heavy or long, attaching it to the camera moves the centre forward and the weight loads the lens mount heavily. When you use the collar properly, the centre of mass is above the screw and the lens mount is loaded by the camera body mass. Note, that momentum matters; the further the center of mass is, the higher momentum the mass generates.
If I see a picture of a lens and it has a collar, what does that mean?
It does that the momentum caused by the lens supported by the body only is higher than momentum caused by the body supported by the lens. When using tripod, use the collar; when carying the camera, hold the lens rather the body.
Presumably it means that the lens is heavy (and probably also large). But does it mean the lens can only be used on a tripod?
It may seem so. The lens can be used as any other lens. When held wrong its weigt can damage the lens mount on the body.
As in, if you use it without a tripod, the weight will snap the camera in half or something?
If held improperly (holding the body only) or attached to a tripod using body mount, it may damage (bend) the lens mount.
Or is it merely that it wouldn't be very comfortable to use without a tripod?
The lens may be heavier than the set lenses. Longer sessions may be incomfortable because you can get tired. It can be hard to shoot with slower shutter as well.
Can I mount 8kg lens to bottom-of-the-range DSLR?
Yes, there is no objection. As @scotbb noted, allways hold the lens by your left hand and support its weight. When using tripod, do small test. Place the camera on a table; If it leans forward do use the collar, if it rests on the body's base you may use the body mount.
Do allways* support the lens with your left hand, no matter what lens you are using - it is code of practice. Pancake or super-tele; it doesn't mind. If I'm using small lens I support both lens and the body with my left hand.
When the lens is supported, there are weaker loads on the lens mount and the camera is more stable.