Output from a digital filter is made up from previous inputs and
previous outputs, using the operation of convolution:

Two convolutions are involved: one with the previous inputs, and one with the previous outputs. In each case the convolving function is called the filter coefficients.
The filter can be drawn as a block diagram:
Two convolutions are involved: one with the previous inputs, and one with the previous outputs. In each case the convolving function is called the filter coefficients.
The filter can be drawn as a block diagram:
The filter diagram can show what hardware elements will be required when implementing the filter:
The left hand side of the diagram shows the direct path, involving previous inputs: the right hand side shows the feedback path, operating upon previous outputs.