The definition of the word 'electricity' is broad. I like Wikipedia's disposition, which was clearly written by someone who was science-minded, and worded carefully to avoid creating more confusion:
Electricity is the set of physical phenomena associated with the presence and flow of electric charge.
Without subdividing the concept, we can't answer your specific inquiries. Physics has many specific and rigorous definitions that do answer your question.
You need to learn the concepts of charge, voltage, and energy. These are all concepts with numbers and units. Additionally, you need to understand current as a flow of charge. Since it's a flow, that is referencing some amount of charge that moved over some amount of time, thus it has units of charge divided by time.
In a similar manner, voltage is energy divided by charge. This reflects the conceptual basis that charge, at some voltage, contains energy. However, for most practical applications, we're more interested in current than charge alone.
Voltage can be said to be a derivative concept of the electric field, but I would ignore this for your level. I would also ignore the atomic underpinnings (which is, btw, that some electrons in a conductor are free to move about). Voltage is the electrical analog for height of a water reservoir, or water pressure. You need to understand that broadly, (charge)x(voltage)=(energy). Put into per-time format, it is (current)x(voltage)=(power). Power is energy per unit time. Light bulbs and fans have power requirements, because they conduct a continuous process where energy is ultimately converted into thermal energy.
I would be extremely skeptical of any purported "understanding" that does not use these concepts such as current, voltage, and power. An explanation might be able to mask the fact that it's using them, but if the concepts are absolutely absent, then the explanation must be wrong. Charge and energy are conserved quantities. That means that they move from place to place, but they do not disappear from our universe. We find relationships that govern those transitions. That essentially sums up all reality as we know it.