Pipeline and real parallelism?
Yes. This is the exactly benefit in use a pipeline. The most simple real life example is a laundry. 

When you just arrive there, you have dirty clothes that you want to "process". You put the first group of clothes inside the washer and wait until it finishes. When it is ready, you get your first pack of clothes and put all in the dryer machine and fetch and load more clothes into the washer in parallel. When the dryer end its job you then start the "folding cycle", releasing the dryer.

I think you get the idea that while you are folding you can load more clothes in the washer and dry more clothes from the washer in parallel.

The main idea in both cases, processor and laundry, are similar: you can do more in less time by doing parallel jobs. 

In the opposite, a processor without a pipeline have to wait all the execution ends to fetch another instruction. Using the laundry analogy again, it is like you only start to wash another group of clothes only after fold all clothes from the first group, wasting time in the middle.