Understanding voltage and current - is there voltage without current flow?
An op-amp has what is known as an input impedance. In the most simplistic terms this can be thought of as a resistance to ground. When you connect a voltage to the input current flows through that resistance to ground.

The "ideal" op-amp has an infinitely large input impedance, which means that an infinitesimally small current will flow - i.e., no current. That never happens though.

The thing to remember is that current is the movement of electrons around a circuit, but voltage is simply the difference in electrical potential between two points in a circuit. Nothing needs to flow for there to be a difference in potential.

Take a simple AA battery, for example. With it disconnected there is no circuit, yet the + terminal is 1.5V higher than the - terminal. The input of the op-amp's input is simply measuring that voltage. But of course, just like in quantum physics, the act of measuring it changes it, because the input impedance isn't infinite, and so some current flows, which then has an effect on the circuit (and hence the voltage) that you are measuring.