Dyslexia is a common learning impairment. It is actually a group of different problems centering around how the brain sees written words and/or numbers, although there are many different permutations.
Dyslexia[]
Generally this refers to problems with spelling, and words in general. Many dyslexics spell very simple words wrongly or pronounce longer words incorrectly. Currently, it is picked up on quite well in schools, and dyslexic children are given extra help to bring their writing skills up to the standards of their peers.
Dysgraphia[]
This is the name given to the poor reading skills exhibited by many dyslexic people. The brain cannot read from left to right and top to bottom across a page. For some people, this becomes so bad that they consider themselves incapable of reading, and never learn properly. For those with a less extreme form, it can lead to amusing incidents when you think you see a completely incongruous word in the middle of a sentence (for example, "Pink Elephant" in the middle of a rather dull paragraph about statistics).
Other types of dyslexic disorders include discalculaea (problems with numbers) and Dyspraxia (problems with memory and balance).
Dyslexia in fanfiction[]
Dyslexia is often misused, misrepresented, or completely ignored in fanfiction. The first two are excuses for bad angst amongst characters, and the last one is used when fanfiction authors want to write about a canonically dyslexic character without dealing with his/her dyslexia. All three are chargeable offences in the eyes of some PPC Agents.
Fanbrats and Dyslexia[]
Many fanbrats use dyslexia as an excuse for poor spelling, grammar, punctuation, and plots. Strangely, the ones who do this seem to be able to spell everything except dyslexia incorrectly, usually in an author's note that reads something like 'plz dont pik on my im dyslexic'.
Dyslexia, however, is not an excuse for bad writing. If you truly have a problem with spelling and grammar, there is nothing wrong with asking someone to beta your fic. Many good fanfiction writers are dyslexic and manage to cope quite well with not butchering the English language.