A patent is a right granted to an individual or group (such as a corporation) which permits the grantee the ability to prevent others from making, using, or selling the invention described in the patent. A patent can be sold, or the grantee may give others permission to use the invention (generally in exchange for royalty payments).
There are three main types of patents: utility patents, design patents, and plant patents. Utility patents are patents on inventions which function in a new way or to provide a new result. A design patent, as its name implies, is a patent on the aesthetic design or ornamentation of something that already exists. A design patent is granted when the design in question does not change the functionality of the object, only gives it a novel appearance. Design patents primarily contain drawings. Plant patents are patents on types of plants that may be reproduced by grafts and cuttings. Note that patents related to genetic engineering of plants are normally considered utility patents. Utility patents are by far the most common type of patents, and are what people normally mean when they just say "patent".
A patent simply gives the owner grounds to prevent infringement through legal means. By itself, a patent cannot stop someone from making or using an invention; it simply gives the patent owner the right to take the person to court if they do.