Electric potential, gradients and equipotential lines

 This video goes through the relationship between electric fields and potentials (i.e. voltage), which are the 2 fundamental quantities created at every point in space around any electric charge. These are abstract ideas, and then there is the math that goes with this relationship - the gradient. 

Check out how to think about a gradient, and how all this relates to equipotential lines and surfaces we talk about in physics. This follows from potential wells we did in mechanics. The gradient relationship is 

E = -dV/dr

So when potential varies through space, there is necessarily an electric field that exists in that space. This also helps explain why electric fields pass through equipotential lines perpendicular - there is no change in voltage along one of these lines, so there cannot be a field or even component of a field along an equipotential line. 

So check it out, there are some details and visuals that hopefully will be helpful.