A patent is actually an intangible, legal right, but many people use the term to refer to the main document prepared to obtain the right.  This is more properly called the "patent application," but when there is little chance of confusion, we'll use "patent" to refer to the document or the right, as the case may be.

Patent applications are complex documents that often seem deliberately written to be hard to understand, but almost all of them can be divided into two much-simpler parts.

The first part, and the one that usually makes the most sense, is basically a technical whitepaper describing the invention.  This part is called the Specification.  The drawings, or Figures, are also part of the whitepaper.  The specification usually includes a lot of information that's already known (or, in lawyer-speak, "prior art.")  This information sets the stage for the description of the invention, and helps (or should help) the reader to understand how to make or use the invention.  It's not required to explain what's so great about the invention, or to compare and contrast with the prior art.  Sometimes it helps to add this material, and sometimes it hurts.  People who are unfamiliar with patents sometimes assume that the patent covers some or all of the information in the specification.  However, the specification is really only present to fulfill a different patent-law requirement: that there be enough information to enable a skilled person to make or use the invention.

The second part of a patent application contains the Claims, which are critical to the meaning and value of the patent.  The claims are what the patent covers — no more, and no less.  Good claims make for a strong, valuable patent.  Bad claims are rarely worth the money spent to get them.  Unfortunately, the claims can be very difficult to understand, and often seem to have little to do with the "invention" you think you're dealing with after you read the Specification.  Part of the reason claims are so hard to read is that there are specific technical rules governing their form, and there are dozens of "magic words" or phrases that are the safest way to express things that come up in claims.  (Some of the magic words are not mandatory, but if you write a claim using different words, you run a bigger risk of getting a bad interpretation of the patent later on.)  Claims that started out clean and sleek and comprehensible when they were filed can also morph into brain-melting, page-long monsters during prosecution, which is the process by which a patent application is turned into a patent.  More information about patent prosecution is in this article.