What is electricity made up of?

In a word, electrons.  These have both the properties of matter and energy, sometimes appearing as subatomic particles and sometimes as a waveform.  Electricity can be classified as either at rest (static electricity) or in motion (current electricity,)  the type we're most familiar with.  Electrical currents are caused by moving electrons subject to the electromotive force (EMF) or the "electric potential," which is created by adding electrical energy to a system, typically by a generator, which typically is a rotating magnet. Experimenters in the 19th century recognized that magnetism and electricity are complimentary manifestations of the same force (where there's electricity, there's magnetism, and vice-versa) and have termed this phenonmena "electromagnetism."  The elctromagnetic force is one of the four Fundamental Forces that define our Universe.