Correlation is a weighted moving average:
Convolution is a weighted moving average with one signal flipped back to front:
Convolution and correlation are the same except for the flip:
Convolution is used for digital filtering.
The reason convolution is preferred to correlation for filtering has to do with how the frequency spectra of the two signals interact. Convolving two signals is equivalent to multiplying the frequency spectra of the two signals together - which is easily understood, and is what we mean by filtering. Correlation is equivalent to multiplying the complex conjugate of the frequency spectrum of one signal by the frequency spectrum of the other. Complex conjugation is not so easily understood and so convolution is used for digital filtering.