The election itself uses a variety of Single Transferable Vote. Very roughly: you rank your top three candidates in order of preference, and initially your vote is counted for your top candidate; if no candidate makes it over the “is elected” line after the initial count, the least-voted candidate is dropped and the votes that were initially counted for them are redistributed to those voters' second choice (or dropped, if no second choice was given); if a candidate is already elected, then surplus votes they don't need are reallocated. This continues until someone crosses the finish line.
There's much more detailed and precise information available from SE's explanation of the voting system (e.g., how does reallocation actually work? [spoiler: interesting math]). On the election page, you can see this in the sidebar if you click on the election tab (currently, you see the nomination tab by default):
In the election phase, up to 10 candidates advance to final community voting. Candidates are displayed in random order.
Any community member with 150 reputation may vote in the election. Each voter may select up to three candidates. Please make your selections in order of preference, with the most desirable candidate as first choice.
We will calculate the winners using OpaVote with the Meek STV method, which automatically weights users' votes in the way that does the most good for the candidates they have selected, in order of preference.
When the election is complete, the ballot file will be freely downloadable from this page for the life of the site. Individual users' voting choices are always private; only the aggregated tally will be made public.