For a variety of reasons, including reducing the sensitivity of the overall gain (closed loop gain) to the open loop gain, reducing nonlinear distortion, stabilizing the (open loop unstable) system, and reducing noise in the system. These are the most important reasons. Other reasons include making the amplifier more linear vs. non-linear (proportional plus integral control), allowing for greater output power before clipping occurs, and reducing the current used by the load when there is no signal present.
In general, negative feedback is used in amplifiers to improve stability and reduce distortion. Stable systems tend to produce less noise than unstable systems. Unstable systems will often "chirp" or "hum" with much higher frequency components if left open loop. The use of negative feedback reduces or eliminates these problems and allows stable operation over a wide range of frequencies. A low-pass filter can also be used after the feedback resistor to limit the high frequency response so that only sound waves with lower frequencies get through.
The simplest form of negative feedback is voltage regulation. In this case, the output of the amplifier is fed back into its input to regulate the output voltage. This type of regulation is usually done using a precision DMM as the error voltage source. The problem with this approach is that it cannot turn off the amplifier, so it is not suitable for applications where you need the amplifier to be off even when there is no signal present.
Because this effect creates a closed loop connection to the amplifier, the gain of the amplifier is now referred to as its "Closed-loop Gain." Then, a closed-loop inverting amplifier employs negative feedback to precisely adjust the overall gain of the amplifier, but at the expense of lowering the amplifier's gain. The gain of an inverting amplifier is thus controlled by adjusting the amount of negative feedback applied.
In general, an amplifier's gain can be thought of as the ratio of the output power to the input power. For example, if we have an ideal amplifier that does not produce any noise or distortion, then the output signal will be the same strength as the input signal. In other words, the gain of the amplifier equals 1. However, if we reduce the input signal, then the output signal will also decrease in magnitude. Thus, if we completely shut off the input signal, then the output would be zero! This means that our ideal amplifier has a maximum gain of 0dB.
Now, let's say we have a real amplifier that produces noise and distortion. If we completely cut off the input signal, then some of the output signal will still be present even though it is being distorted by the noise produced by the amplifier. Therefore, the maximum gain of this amplifier is less than 0dB.
Finally, let's say we provide very little feedback, so there is no connection between the input and output signals.
Because of their high gain sensitivity in the absence of feedback, op-amps make circuit design challenging. In this figure, the closed loop gain has a constant gain from DC to 10 kHz (which depends on the frequency response of the op-amp). As seen by this example, utilizing feedback offers bandwidth to an amplifier. The most common use for feedback is to increase the low-frequency cutoff of an amplifier.
The purpose of adding feedback is to reduce the high-frequency gain of the amplifier. If this were not done, then signals with frequencies higher than about 1/2 of the op-amp's maximum rate would be amplified too much. This could cause problems for high-frequency signals that are being amplified.
Op-amps have very high current gains so small changes in voltage can change large currents. This means that even slightly different inputs will cause the output to change greatly. Adding feedback allows more accurate control of the output signal.
Also, feedback gives the amplifier its own "memory" of what was last connected to its input. This allows the amplifier to reproduce the original signal later when it is reconnected to the network it was part of. For example, if the amplifier had been used as a speaker driver, then disconnecting the speaker would stop it from sounding for a few seconds while the amplifier stopped responding to the disconnected button.