Because the speech signal is discursive and transient, memory must retain it until decoding takes place.
But for now we must acknowledge the role of memory specifically in the auditory process. Two things are critical in audition. The auditory stimulus is transient, and the message is discursive. That means the signal is strung out in time. It doesn't hang around long enough for us to experience the entire message in one "sitting," like we can when we observe a picture.
In audition, it remains for the processes of memory to hold on to the pieces of the stimulus that have faded, so that we can deal with them as if we had the whole. Note that I said processes (plural), because memory (like language) is a system of many sub processes.
Of the many memory sub processes, we will mention two for now: Short-Term and Long-Term memory.