Rigurously, voltage are differences of electric energy per unit charge.
Let's explain.
'1) The easiest way to start is thinking about electrostatic potential energy. An electric charge has a certain electrostatic potential enegy for the fact of being immerse in an electric field.
This is very analogous of gravitational potential energy. A stone has a certain energy for the fact of being subject to gravity. Specifically, for a stone of mass $m$ placed at a heigth $h$, the potential energy is $E_{pg}= mgh$, as you know.
If there were not gravity, the stone would have no energy.
In the same way, if a charge is in a region with electric field, the charge has a potential energy.
'2) The main property of gravity is mass. The main property of electicity is the electric charge.
We can define "potential energy per unit (characteristic property)". This is called ""potential"
Gravitational potential is gravitational potential energy per unit mass: $\phi_g=\frac{mgh}{m}=gh$
In teh same way, electrostatic potential = electrostatic energy per unit charge: $$\phi_e=\frac{E_{pe}}{q}$$
So, that's electrostatic potential: the energy per unit charge.
- Voltage are differences of potential
So $V=\phi_1-\phi_2$.
This is kind of the same as a waterfall of a power plant.
We don't actually care if the water falls from 2200m to 2000 m, or if it falls from 1540 to 1520. What we actually care is the difference in heights, because then
$\Delta E_p=mgh_2-mgh_1 =mg(h_2-h_1)=mg \ \Delta h$
The energy that we can exctract from the waterfall is due to that 20 m difference, regardless of how high we are. So we care about potential differences, not just potential.
I hope this example helps.
Note: there are more sources of potential besides the electrostatic one, but that's more complicated.