First I thought order of featured tab is post modified time order. But seems like I am wrong.
So what is the order of featured tab?
Super User has a good number of bounties right now and they appear to be in a strict, "soonest ending" order.
Clicking through them (hover over the "ends in ___" to see the ending date/time) shows that even the bottom two, both expiring in 7 days, appear in the opposite order you would expect if the blog post were correct. The 500 reputation bounty ends last at 17:45:26 and the 50 reputation bounty ends mere seconds before it at 17:45:01 and is indexed first, despite the claims of the blog post.
So... it seems that:
Note, this excludes the new navigation that has been implemented on Stack Overflow, which allows you to sort by several different factors.
The default sort on SO seems to be biggest first, no consideration of expiration date.
This seems to conflict with this blog post from 2011 which implies that it's a combination of two things.
The top results are the bounties expiring within the next 24 hours, by soonest expiration time. After that, bounties with the highest amount are prioritized.
The featured tab on the homepage gives priority to larger bounties. The last 24 hours of the bounty period are still ordered purely by time of bounty end, but up until then the larger the bounty, the higher your question will appear on the featured tab.
I couldn't find any explanation for it changing, though.