What Are Linear and Circular Convolution?
Linear convolution is the basic operation to calculate the output for any linear time invariant system given its input and its impulse response.

Circular convolution is the same thing but considering that the support of the signal is periodic (as in a circle, hence the name).


Most often it is considered because it is a mathematical consequence of the discrete Fourier transform (or discrete Fourier series to be precise):

One of the most efficient ways to implement convolution is by doing multiplication in the frequency.
Sampling in the frequency requires periodicity in the time domain.
However, due to the mathematical properties of the FFT this results in circular convolution.

The method needs to be properly modified so that linear convolution can be done (e.g. overlap-add method).