I want to burn a CD from iTunes and include a picture of my own as the cover art. So then when people stick the CD into their computer, it shows a picture in iTunes in the cover art section.
CD do not contain any image anywhere. What happen when you insert the CD is that iTunes looks at the number of songs, their length, the length of silence between song and derives a number from it. It then asks the iTunes Store to find if a CD with this pattern exists. If it does the iTunes Store returns the cover art and all the metadata about the CD (Artist, album name, song names...).
For CDs you burned yourself you can't provide this information to iTunes just from the CD. Unless you find a label to release your CD to the masses and then Apple will add it to its list.
There is a format called CD-Text that allows you to include track data (but not cover art, AFAICT), and iTunes lets you enable that format as an option. In the screenshot bmike posted, you can see "Include CD Text" as an option under Audio CD--that's how to enable this. I just tried it on my machine and the option is grayed out--apparently not all drives can write this format.
This wikipedia article has more information and lists a number of programs that can burn the format.
Whether the recipients of the disc can do anything useful with the extra information is another question.
If you burn the songs as a Data Disc or a MP3, iTunes includes the music files with the correct tags. If your songs have artwork embedded into the song files, your friends will get all the information and artwork you have prepared for them without needing iTunes to retrieve the artwork as a second step.