Parody is known as one of the highest forms of both comedy and flattery. A parody takes the elements of a subject and changes them for some comedic purpose- it's almost like a 'second dimension' if you will. It is a close relative to satire (poking fun at) and pun (elaborating with something similar).
While Weird Al's career is not limted to parody, it is what is he is most known for.
Parody examples: Like a Surgeon, Amish Paradise
Every artist has a particular style (musical, lyrical, etc) in which they express themselves. It is this style that is the target for parody. It's an indirect parody because only certain aspects of the song are targeted rather than the whole thing.
This is a term Al himself coined up, and because he uses lyrics that are not patterned after any particular song, this is sometimes called an original.
Style Parody samples: Dare To Be Stupid, Frank's 2000" TV
A true Al original is a song or idea which is 100% Al's. No music or idea is being played upon, thus making it a true solo creative effort on Al's behalf.
Sadly, most of the general public thinks that Al doesn't even do originals!
A few True Originals: I'll Be Mellow When I'm Dead, UHF
Purists consider this plagerism, but almost every respectable artist (even those without respect) have done this. A cover is when an artist re-records someone else's recorded song in their own personal style. The cover will often change the musical arrangement or mix in order to make his version a little different than the previous.
Personally, I don't know why Al does them- they're not particularly my favorites (with the exception of Bohemian Polka).
Some of Al's Covers: George of the Jungle, Money for Nothing/Beverly Hillbillies
These are the songs or sketches released on record that were written especially for various television, movie, or other projects.
While Al primarily works alone and for himself, he does do side projects, like Spy Hard, for others.
Custom Al specials: This Is the Life (Theme to the movie Johnny Dangerously), Harvey the Wonder Hamster
Self-explanitory. These were spoken, not sung.
Hear Al speak: Peter and the Wolf, Poodle
Sometimes mistaken as a style parody, this is actually the real thing! These are real polkas folks!
With the exception of Bohemian Polka & Polkamon, all of Al's polkas are medleys of unrelated songs that are/were popular at the time they were released. If you ever see Al live, he does a medley of his *own* songs (non-polka style)!
Al Polkas down with his bad self: Hooked On Polkas, Bohemian Polka