In a nutshell:
The dyslectic person is using his right hemisphere instead of his left to read and spell.

In great detail:
The two most important contributers to dyslexia are an underutilized left-hemisphere, and an out-of-whack central bridge of tissue in the brain, called the corpus callosum. (The bibliography contains technical details from some of the brain-scan research which has documented these two problems.) But why does it matter which side of the brain you use? Because the left-hemisphere is programmed to do the things you need for reading and the right is not.

The left can:

• match a letter with its sound,
• handle information that comes into your brain in strings, like the sounds in a word - one letter after the other, rather than seeing a word as a single picture,
• separate a word into its individual sounds, and
• understand grammar and syntax.

The right hemisphere is different. It deals in areas and space and patterns. It doesn't understand parts of speech, or keep track of letter-order in spelling. It "reads" a word as a line drawing that it has been taught has a meaning, -- a sketch, not a line up of sounds. So if it sees this: 

  or this:   

it knows that these "drawings" represent a place where somebody lives. But it is just as apt to say home or residence (or igloo or tepee) as house. You can see that if the left side leaves the reading to the right side, the result can come out scrambled eggs.

As to the corpus callosum, it is a bridge of nerve cells over which information from one side of the brain gets to the other. Everything you see or hear goes to both sides, but each side has it own specialty. The corpus callosum not only transfers information, it helps decide which is the appropriate side, and sends it there. Obviously a wimpy CC may not deliver language tasks to the left where they belong. On top of that, it transmits slowly, so part of the information arrives out of sync with the rest. (See the "Jigsaw Puzzle")