Property rights can be generally defined as the set of actions which an individual may perform upon an object which will not lead to reprisals from the
powers that be. This is usually the government, but if an area has no government, it means the stuff the person can do to the land, buildings, and
stuff without the bulk of those around him trying to stop him.
Well, even that is a bit of a light definition. Part of the problem is due to the fuzzy nature of the word right in the first place. There is some disagreement what are natural rights, artificial rights, and even whether or not there is such a thing as a natural right in the first place. Some say might makes right, in which case, if you got the guns to do what you want, those are the rights you have. If you don't, you don't have the right to remain silent, you don't even have the right to keep breathing. Others say rights come from God, and carry moral force as such, and violating rights is a sin. And it's not like anyone ever disagreed about religion, is it?
For practical purposes, property rights are the things the government lets you do with what it and you both agree is your property.
Addendum
Cletus the Foetus suggests "set" or "domain" instead of "collection" of actions. I agree.