A lipogrammatic text is one that's contrained by the omission of one (or a group of) letters. Perhaps it's easier to demonstrate the possibilities of the form by giving you a few examples:
- Georges Perec's 1969 novel, La Disparation (translated as A Void) runs for approximately 300 pages without using the letter E (the most common letter in French). Gilbert Adair pulled off an amazing feat by translating the original as A Void in 1995, remaining faithful not only to the storyline, but also its linguistic restriction. Perec wrote several additional texts in this fashion, including the shorter novella, Les Revenentes (translated by Ian Monk as The Exeter Text: Jewels, Secrets, Sex).
- Walter Abish's 1974 novel, Alphabetical Africa, contains 52 chapters, the first of which only contains words beginning with the letter A, the second, words beginning with A and B, and so on until, in chapter 26 any and all words are permissible. Abish then starts taking letters away again, starting with Z, until the final chapter which, once again, consists solely of words starting with A.
- Christian Bök's 2001 book (its genre is ambiguous) Eunoia, which consists of five chapters, each named for one of the vowels and comprised solely of words containing that respective vowel. In addition, Bök has instituted several other rules, including making use of at least 98% of all existing words featuring the given vowel, as well as specific tasks, including writing about the act of writing, a feast, a debauch, a nautical journey, etc.
The purpose of such writing exercises is two-fold: first to provide restrictions that might ultimately yield worthwhile work, and second to force the writer to avoid common words and phrases and/or discover atypical language to suit their expressive purposes. For your final prompt, I'd like you to write a poem that's restricted in some lipogrammatic fashion but I'll leave the specifics up to you: you can chose to avoid a certain letter or group of letters (one possibility: choose a brief word and avoid all those letters), to use only one vowel or to narrow your restrictions to words beginning with certain letters; you can also shift your restriction from stanza to stanza (or section to section) as you see fit. Be sure to note what restriction you set for yourself when you post your poem.