I became aware of the energy thing only recently and it's driving me nuts. I've become a bit of a dilettante as far as Duolingo is concerned. I made my account private because I'm very competitive and trying to keep my place in the leagues was taking too much of my time.
I try to do at least a lesson a day to keep my streak up, but sometimes I forget. Then I have to use my gems to buy a streak freeze.
► Show Spoiler
Streak freezes cost less gems on the website than on the phone app, so I always buy gems on the website via my laptop.
When my gems are getting depleted I go to the Free Chest on the phone app and "watch" ads (or let them play while doing something else
) and I wondered why the heck watching ads was filling up my energy instead of my gems and what the heck is this energy thing. That's pretty much when I became aware that energy had replaced gems. Only when your energy gets back up to a certain level do your gems start to be refilled.
Then I noticed, as others have observed, that even when I do a perfect lesson I lose energy and I wondered what the point was. Correct answer streak or no I end up with less energy at the end of a lesson than I started with. It's the most demotivating thing ever and I guess intended to get us to pay for DL.
There are lots of other changes to DL that are getting me annoyed and demotivated but, after all, this is the thread about energy. 
By the way, if you want to use your phone and not lose energy, DL on your web browser still has hearts. For me, anyway.