Voltage is electrical potential energy per charge, i.e. EPE/q. If moving an electron from Point A to Point B takes 1 electron volt of work, then the voltage difference from A to B is 1eV/(-1e) = -1V (note that the notation is a bit confusing, as the 'e' in 'eV' stands for "electron", while the 'e' on the RHS stands for "elementary charge"). Conversely, if an electron travels between two points with a voltage difference of +1V, then it will perform 1eV of work.
If we define current as the signed flow of charge, then a positive charge traveling from the positive terminal to the negative terminal is a positive current from the positive terminal to negative. A negative charge flowing from negative to positive is also a positive current; the negative sign from going the opposite direction and the negative sign from opposite charge combine to give a positive current.
"Positive" and "negative" are a bit misleading, as there's no "absolute zero" of voltage. The "positive" terminal is simply the one with the higher voltage, and the "negative" one is the one with lower voltage.
If one Coulomb of electrons travels from one terminal to another, and the second terminal has a voltage that is 5V higher than the first, then we have -1C of going across -5V of voltage, giving (-1C)(-5v), or 5J, of work. The electrons do work by being negative charge going across a negative voltage difference.
As something that's somewhat analogous, if you release a helium balloon (negative weight), it will float upwards, and the work done will be the weight of the balloon times the signed change in height. Both the weight and the displacement will be negative, giving a positive amount of work done by the balloon.