Here is the explanation from TiA's site, with me mixing in some of my explanation:
Simulation Methodology: Monte Carlo simulation-random numbers applied to normal distribution for 5000 election trials.
Win Probability is pct of simulation trials Kerry wins (at least 270 EV).
This is the core idea behind Monte Carlo analysis. TiA wrote a computer program to make a "good guess" at the likely election outcome. If we make one good guess, it's probably wrong. So TiA uses "Monte Carlo analysis" and makes 5000 runs of simulated elections. They are "random"-ized which means made to vary a bit at the whimsy of chance like flipping a coin. That way, each guess comes out different a little bit, but each is a good guess. Then he reports the percentage of simulated elections Kerry won in his model. If this number is high, and the other parts of the model are done right, Kerry will probably win. Monte Carlo has a long history.
The Monte Carlo percentage is not the predicted vote. It is how many of our good guesses were "Kerry wins." If 85% of the results are "Kerry wins", that means Kerry lost 15% of the simulated randomized elections.
What it could mean is that the election is going to be very close, but that there are 85 chances in 100 that Kerry will get at least 1 more electoral vote than he needs. It does not mean he will get 85 percent of the electoral votes themselves or 85% of any ballots cast in any simulated election. It represents a prediction on the "one or the other, which is it going to be" scale.
Project Kerry pct of state popular vote. Nat % based on total state votes.
"Project Kerry" is a subject-verb clause, like "Make a projection about Kerry."
This goes with some details above that specify the random numbers are generated for each state's result, a different random number for each election.
A 'random number' is like what you would get if you flipped a penny 10 times and counted the heads. You would get a number from 0-10, but probably 4,5, or 6.
It would be weird if you flipped the penny 10 times and it was 10 heads or zero heads, but that could happen, right?
This kind of "distribution" of random numbers is called "normal." By "distribution", people sort-of mean: If you had to tally the results of trying this a lot, how would the outcomes be distributed among the possibilities, where the possibilites are 0-10, but they aren't all equally likely to happen?
4,5,6 would get a lot more of the distribution than 0,1,9,or 10 do.
If you draw a graph of this sort of thing, it's a bell curve, with the low parts over 0 and 10, and the high part over the 5.
For this election, TiA does something really similar, but 'lines-up' the bell curve over what the polls claim Kerry is getting for support. So the "average" result for each state should match up well with the polls, but randomly wobbles around their prediction for each trial.
So it is the normal curve part of his program that prevents too-crazy outcomes like Florida voting 90% for Kerry. Although out of 5000 simulated elections, that could happen a couple of times. Those would be some of the bad guesses that Monte Carlo averages out, probably, but a strength of Monte Carlo is that it incorporates the
possiblity of freakish coincidences.
Normal Distribution calculates Kerry state win probability, based on mean poll value and Std Dev 4.0% MoE/1.96.
This has to do with the shape of that bell curve/normal distribution. This essentially says where the 0 and 10 are going to end up. Polls don't give enough data to measure this, so TiA does a great job of getting it back from their published Margins of Error, which is a related concept.
OnEdits: Seasoned with punctuation and math corrections till it tasted better to me. ;)