I hope to write an article by this title (“What is an electron?”) someday. That’s my dream!
The nature of electron is a mystery. The fact that we can build a civilization based on the manipulation of electrons without knowing the ontological status of electron is a deeper mystery. Electron has 3 basic properties: charge, spin and mass. We can measure these properties but we don’t understand them.
Most professional physicists ignore the hard questions and sweep them under the rug and pretend there is no mystery. I am glad there are physicists like Frank Wilczek who recognize the mystery of the electron. He wrote a short article without any formulas titled “What is an electron?” which can be found here.
The published version of that article appeared with a different title: “The enigmatic electron” (Nature Volume:498, Pages:31–32, Date published:06 June 2013). The Nature article is behind a pay wall.
Frank Wilczek shared the 2004 Nobel Prize in Physics with David J. Gross, H. David Politzer for the discovery of asymptotic freedom in the theory of the strong interactions.
At his personal web site http://frankwilczek.com/index.html Frank Wilczek has many more articles focusing on the fundamental questions.