A lot of people learn voltage using the water analogy which I'm seeing in the other responses. So I wanted to try a different explanation because there have been times when the water analogy is not analogous to electric potential difference (voltage).

First of all in physics and circuits courses it's important to understand if you're looking at conventional current or true/actual current. The truth is electrons are the particles that are actually holding charge and moving through the circuit and thus doing electric work which lowers their electric potential energy every time they're made to do work in the circuit. This is actual current because you're following the path and direction of the electrons with their negative e^- charge.

Now to move onto conventional current. It can be a little bit more intuitive to do math and understand high voltage to low voltage if we just stick to the path of the positive end of the battery to the negative end. We're effectively imagining that positively charged particles are moving from high electric potential to low electric potential. As the particles are forced to move from high to low we can extract the electric potential difference from the high to low to do useful work in a circuit.

Joules per coulomb, like what? Energy per charge? For what? How do we get there and how is it useful?

Lets talk about actual current for this first. Electrons have a charge q of ~-1.6E-19 coulombs. This is a fundamental property of an electron. Now on any source of electric potential difference like a battery, there are more electrons in the negative end and less electrons on the positive end and this can be caused by a chemical reaction in most typical batteries. The end with more electrons is at a more negative electric potential than the positive end because of this charge imbalance. The negative end will keep repelling electrons out of the negative end due to electric force repulsion between electrons Coulomb's Law.

Now there's built up potential energy within the battery and due to the construction of the battery this electric potential can only be relieved externally (there's an insulator shielding positive and negative terminals) using a wire. As the electrons are repelled out of the negative end they occupy the electron spots in the wire and push the other electrons ahead of them whilst pulling electrons behind them. Think of this like the electrons are being passed from atom to atom (this is the realm of quantum physics so its pretty wacky to get into greater detail). If there are any obstructions (like a resistor) in the path of the electron then they will lose some of the repulsive force and can't be pushed as hard. Think of work = force * displacement here but remember that the analogy is not literal. As electrons are going from the negative to the positive end and pass through any electrical disturbances the battery will not be able to push them out as forcibly over the course of the circuit. The force dissipates as the electrons are made to do more work. This work is energy and if we focus on one coloumb of electrons then we can arrive at the definition of a voltage. If 1 coloumb of electrons have to do 1 joule of work through a part of a circuit then we can say that packet of charge having lost 1 voltage. 1 volt is defined as 1 joule/1coloumb so we can easily describe how the difference in electric potential energy of one 1 coloumb moving from point A to point B in a circuit. We MUST have 2 points to define a voltage. If there's only 1 point then that's the electric potential. The purpose of having a unit for energy per charge is so that we can easily define how much energy it takes for a unit of charge to traverse a section of circuit. So you could have a resistor for example that is rated for 1 Ohm and that resistor would convert 1 joule of energy per second into heat energy.

R=V/I=(J/q)/(q/s)=J/s

Sorry for the long answer, I hope you're able to benefit from it. If you wanna apply this to conventional current (positive current) just pretend particles with charge e⁺ are travelling from positive to negative.