Pipelining simply means to overlap an repeated sequential execution. For instance, assume that the steps S[1]; S[2]; S[3]; S[4] were executed in an infinite loop. Then, the simplest form of pipelining would mean to start the next loop iteration after the first step of the previous iteration has terminated, i.e., we have the following execution where each row corresponds to one loop iteration and the columns are the steps in that iteration:
time 1 2 3 4 5 6 7
S[1]; S[2]; S[3]; S[4];
S[1]; S[2]; S[3]; S[4];
S[1]; S[2]; S[3]; S[4];
S[1]; S[2]; S[3]; S[4];
As can be seen, after the first 3 steps, the pipeline is filled, and now we execute S[1]; S[2]; S[3]; S[4] in parallel (instead of a sequence). However, note that the steps S[1]; S[2]; S[3]; S[4] in the pipeline refer to different loop iterations.
PIpelining is not only used in hardware designs (where it is frequently used), but also in software, where it is sometimes called software pipelining. That is an important compiler technique that statically scheduled processor architectures are using to find more parallelism for the execution of loops.
The filling phase is often called the prolog, and the phase where the pipeline may terminate is called then the epilog.
It is however not required that the next iteration starts one step later. In particular, it is even sometimes required that the next iteration has to start later than that to avoid conflicts. Then, you may have instead a picture like the following below which is still pipelining:
time 1 2 3 4 5 6 7
S[1]; S[2]; S[3]; S[4];
S[1]; S[2]; S[3]; S[4];
S[1]; S[2]; S[3]; S[4];
S[1]; S[2]; S[3]; S[4];
Clearly, there is less parallel execution in this case, so the initiation interval (which is the time gap between two starting iterations) should be as small as possible.
