Operational amplifiers are versatile analogue microchips with many applications.
Here is a page summarising many standard op amp circuits.

NON INVERTING V_n: If a signal is applied only to the non inverting input, if the input voltage rises, the output voltage also rises.

INVERTING V_i: If a signal is applied only to the inverting input, if the input voltage rises, the output voltage falls.

BOTH INPUTS: The op' amp' amplifies V_n - V_i   
This is called a differential amplifier because it is amplifying the difference between V_n and V_i
This type of amplifier is useful because it cancels noise arriving equally to both inputs while amplifying the wanted signal.