I feel like there's a lot of partial explanations in this thread.
The rating system being used is Bayesian ELO and it works as follows:
1) The system looks for any player who has less games than the amount of games they specified they want to play. It then pairs up players (probably according to their rating, but that is Fizzer's code, not the BayesianELO program so I'm not 100% sure)
2) For any game you complete, the system takes your rating and your opponent's rating into account when calculating the new ratings. This is what happens in regular ELO as well.
3) Next, the system takes your and your opponent's rating variance into account. Your rating variance can be seen as the uncertainty of your rating. If you've played one game, the system will give you a high variance. Here's two examples to illustrate. In both you have only completed one game:
3-1) You beat the lowest rated player on the ladder. His rating is 495. The system now gives you a rating of 638. However, it also says you could be anywhere between 60 and 1216.
3-2) You beat the highest rated player on the ladder. His rating is 2302. The system now gives you a rating of 2446. However, it also says you could be anywhere between 2054 and 2830.
The more games you complete, the lower this variance gets.
4) The ladder also updates globally. It makes sure the offset rating is 1500 and takes into account how the ratings of your past opponents have changed. If someone you played has risen in rating, you will probably profit a tiny bit from this. The converse is also true.
Another note that needs to be made, is that Warlight will give you a small advantage for getting first pick. In chess, this advantage is considered to be around 33 ELO points; for Warlight it's assumed to be 10 ELO points.
ELO points are a handy tool to predict the chances of winning. If an infinite amount of games were played for all players, this would be the win chances based on ELO-difference:
Win percentage ELO-difference