A patent is a Government-granted exclusive right, or a set of specified rights, to an inventor, or a person who claims to be the true and first inventor (or the discoverer of a new process) to make, use or sell an invention, usually for a specified term. It may be granted for such novelties, (criteria for which are defined in law), as

a) A process or method that is new, useful and not obvious.

b) A new use of a known process, machine, or composition of matter or material, including asexually produced plants and genetically engineered organisms. 

c) Any new, original, and ornamental design for an article of manufacture.

By such a grant of temporary monopoly to the originator, patent law aims at stimulating inventive activity and rapid realization or exploitation of new inventions for public benefit. As such, a patent falls in the same category of intellectual property issues like copyright and trademarks.

The patent is a personal property: so it can be sold, assigned or transferred as deemed by the owner. As such there can be disputes, in which case the authority or jurisdiction concerned has to mediate and investigate infringement if any and grant penalties to the violator / damages to the rightful owner.

A little history

The term patent derives from "letters patent" or the open letters by which a sovereign traditionally conferred a special privilege or right on subject. The first recorded patent is that granted to architect-engineer Filippo Brunelleschi in 1421 in Florence for an industrial invention. Since then countries had set their own norms to grant patents including the duration. For example, France granted a short term when the nature of the patent invited overall general use. The erstwhile USSR, indeed, most communist countries, didn't believe in them, certificates sufficed as recognition of the inventor's work. US and Canada granted patents for 17 years from the granting date.

Thomas Alva Edison probably has the greatest number of patents to his credit - as many as 1093, including the incandescent lighting system - an improvement of an already extant, 50-year-old idea of the light bulb, (evolving his designs after purchasing an 1875 patent from its inventors, Henry Woodward and Matthew Evans). It would be another 30 years before the cost-effective tungsten filament was invented and came into widespread use. (Inventions of Edison)

It's only in the 1990's that establishment of WTO (World Trade Organization) brought along with it a common minimum set of rights that should be granted to all patentees by governments, as well as a period of 20 years (from the date the application is filed) as the term of the patent.

Interesting historic patents can be found at list of historic patents. More information on historical patents can be found at this list. A source for unusual, "strange or intriguing" patents is Delphion's Gallery that lists several "obscure" patents.