While I get what you're describing is the realization that electrons have mass, I want to clarify that they are still energy. Everything is energy. Mass is a kind of energy. Or rather, a rest mass is a kind of energy. All mass is energy and all energy is mass, but rest mass is a special kind worth distinguishing.
At a fundamental level, everything is in a sense "naturally" massless particles (which are actually just excitations in energy fields, of a fundamentally wavelike nature, yet still in discrete units and so kind of particle-like too) propagating at c. It's just when those particles/waves/excitations interact with each other (or strictly, with other fields, whether those are manifesting as particles or not) that they stop for a moment to do that interaction and then continue on, such that an ongoing interaction causes them to drop below c in aggregate, and the kinetic energy lost in that slowdown hangs around the place where they're interacting, which manifests as the kind of energy we call rest-mass.
This is what that Higgs boson thing you've probably been hearing about was all about. Most of the rest-mass of ordinary matter can be accounted for from the electromagnetic and strong and weak nuclear reactions bindings quarks together into nucleons, binding nucleons together into atoms, and binding electrons into orbit around them. There's a lot of energy stored in keeping all those particles/waves/excitations hanging around together instead of flying apart at light speed, and that's most of what we measure when we measure the mass of ordinary matter. But even after we've blasted ordinary matter down to those constituent fundamental particles and isolated them so they're not interacting with anything we've accounted for yet... they're still moving below c and they still have rest mass. So there's a question of what the heck they're interacting with once we've ruled out everything we know of, and the theoretical answers was an unknown field named after Higgs. And supposing that field exists, it should be possible to produce excitations in it -- to make particles come out of it -- if we "shake it up" vigorously, so to speak, in a really high-energy event. The Higgs boson is the name of the particle that should manifest when the Higgs field is excited, thus proving that there really is a Higgs field there, and explaining why free electrons have rest mass even when they're not interacting with anything else we know of.
A lot of other properties of those fundamental particles also change in the process of slowing down below c and they essentially become different particles than they were. The 'fundamental' particles with mass that we know of are in some sense not really fundamental, but rather they're what more-fundamental particles become when they interact with the Higgs field, slow down, acquire rest mass, and change in a variety of other ways.
TL;DR: Everything is energy, and when some bits of energy slow down to interact with each other, that slowed-down energy hanging around one place is what we call rest mass.