I believe that MySQL evaluates from Left to Right, so first rows are filter based upon "a" then that temporary table is filtered against "b" and the result is given.
You can always define which way will be done by using a sub-query:
SELECT * FROM (SELECT * FROM `table` WHERE a=1) WHERE b=1
Essentially you're forcing MySQL to first generate a temp table of items where a=1, then you're filtering on that temp table where b=1. You could also switch it if you needed.
And for your own edification, here is the MySQL WHERE optimization entry.