How electron and energy related together?

The first electrons indicate their energy by their motion and they can have any (not infinite) value of energy, different of zero. When an electron is confined and bonded in a limited system (as an atom for example), it can have only well defined values of energy (discrete levels), determined by Quantum Mechanics (permitted by the solutions of Schrodinger equation ).

Electrons and energy are related because electrons can possess energy due to their movement within an atom's electron shells or as they move through a conductor in an electrical circuit. The energy of an electron can change when it absorbs or emits photons or when it interacts with other particles or fields. Additionally, electrons can carry energy as electrical energy when they flow through a conductor, which can be converted into other forms of energy such as heat, light, or mechanical energy in various devices.