AJM pretty much hit all the bases as far as the numbers go, but I want to expand on some mechanical changes. I would wager that most of the offensive production changes we see are more due to a change in approach than a change in his swing. That being said there are some key changes in the swing that have helped lead to his highest HR/FB since his rookie season in 2009.
Elvis has always had a very mechanically sound swing that is built for driving the ball hard into LF, but for whatever reason between 2010 and 2014 his pull rates were extremely low and his ground ball rates were astronomically high. His "drive the ball" swing was still there and he showed it from time to time, but for the most part he was content keeping his bat level through the zone and keeping his hands inside the ball to put it the other way. In 2015 we saw a massive shift in approach, but the results didn't follow. In 2016 the swing resembled a more refined version of 2009 Andrus with a high leg kick and mechanics that aren't meant to dribble the ball through a hole.
The Small Changes
The first thing is Elvis now has a great deal more coil in his pre-pitch load. The first picture here is from 2014 and the second is from 2016. The leg kick is another difference, but focus on how much more exaggerated his coil is. The point of doing this is to create the maximum amount of tension in the core so at the point of the uncoil the hitter has an extra amount of stored energy to help generate bat speed.
To show you the good parts that have always been there; this next .gif is Elvis at the ripe old age of 20.
Lower body gets engaged with very sound mechanics and weight transfer, the back elbow gets tucked in for great bat angle to drive the ball on a line or in the air, hips pull a mostly extended front arm around for solid bat speed. There are a few main differences I see in this swing and his 2016 swing; the load is extremely minimal and doesn't create any tension in the core, his swing isn't putting much separation between the hips and hands which leads to much of the power his lower body is generating being wasted, and his lead arm is even more extended in 2016 which allows his hips to pull the bat through the zone for extra pop.
It's easy to see why scouts loved the swing early in Elvis' career and fully expected him to hit for average and power. Somewhere along the way, before his swing matured into his natural strength, his approach shifted away from driving the ball. In 2015 Elvis decided to make the adjustments to the approach and over the next year refined his swing and now we are seeing the benefit; a swing tooled for driving the ball.
If you had asked me a year ago if I thought Elvis would put it together I would have said no, but Elvis bought into hitting the ball hard and made the necessary changes to bring it to fruition. Even better, I don't think his stats this season are in line with how good his swing is right now.; it wouldn't surprise me at all if Andrus puts up 12-14 home runs next season.