First, a classic op amp amplifies the DIFFERENCE in the voltages at the + and - terminals.
First and a half, an op amp has a VERY high voltage gain.
Second, every linear circuit that uses an op amp provides a feedback path from the output to the - input.
This creates a control loop, where the whole point of the feedback path is to drive the difference between the two inputs to zero. In normal operation, the op amp in circuit actively drives that difference to zero. For analysis of the circuit, then, it is generally good enough to assume that the difference is zero.
Start with the classic noninverting buffer stage, where the input is fed to the + input and the output is tied to the - input. The only output value that will yield zero difference is Vout = V+ (the voltage at the + input).
Consider the classic unity gain inverting buffer, where the + input is tied to ground, the signal is applied through a resistor to the - input, and an equal resistor ties the - input to the output. The op amp will try to drive the - input to ground. If the input signal is above ground, current must flow in the input resistor, and attempt to flow into the - input. This would induce an offset voltage across the op amp input impedance, which is amplified by the op amp, and that gives rise to an output voltage, which in turn gives rise to current through the feedback resistor. If the current in the input resistor is equal to the current in the feedback resistor, then there is no current left to induce an offset voltage at the - input, and the amp is happy.