An inverting amplifier uses negative feedback to invert and amplify a voltage. Negative Feedback is the process of "feeding back" some of the output signal back to the input. The Negative feedback is achieved by bringing a fraction of the output signal to the inverting input of the op-amp by using an external Feedback Resistor called Rf.
The Rf resistor allows some of the output signal to be returned to the input. The presence of the negative sign is a convention indicating that the output is inverted. For instance (see picture), if Rf is 2,000 Ω and Rin is 200 Ω, then the gain would be -2000Ω/200Ω, which is -10.