Abstract
    A paragraph or so describing the invention.  [This part of the patent application is non-binding in the sense that it does not define the invention. The abstract is generally only used to assist people in searching for relevant inventions.]

Specification
    Several sections describing the background of the invention, describing the state of the prior art and how this invention is distinguished from the prior art, as well as the "best mode" (my favorite embodiment).  I reference the invention's drawings (if any) here, explaining what each part does.

Claims
    This is the key part of any patent because it defines the legally protection portion of the invention.  The claims are numbered, some depending on previous claims (the whoosy-whatzit described in Claim 1, further comprising...).  Claims are either independent or dependent.  The easiest way to think about claim structure is by a tree (although they are always printed as a numbered list).
 

Claim 1 would be called the "independent claim."  It is the broadest claim.  Claims 2 through 6 are "dependent claims" because they include all the limitations of Claim 1 as well as some of their own.  For example, Claim 6 includes the limitations of Claims 1, 4, and 5.  Because Claim 1 (or any independent claim) is the broadest, it confers the most rights.  If a product does not infringe Claim 1, it cannot infringe any of the other claims either.

Drawings