Good motivation for parallel data structures and algorithms
The quintessential example is large-scale physics simulations, say "electronic" wind tunnel or protein folding (i.e. "finding new medicines"). Both are hugely expensive in terms of computation cost, but yield themselves well to parallelization.

Another area in which parallelization is important is "big data", say search engines. When dealing with big data you need to divide the work among many processors. However often in these cases, most of the work is done in an "embarrassingly parallel" fashion, in which each processor does its share of work, and everything is combined in the end; you could (but don't have to) argue that this is not an interesting example for parallel algorithms.

Yet another example is computer animation, say for the movie industry. This example probably has the same shortcoming as the previous one.

What is common to all three examples is that computation is very costly, and cannot be executed sequentially within a reasonable span of time. Hence the need to distribute the work among several computers (or processors, or cores).

Another possible use case is when you want answers really fast. Here an example could be real-time cryptanalysis during a war: you want your answers in one hour rather than one day, and it makes a big difference. A similar example is real-time TV studios, which probably benefit from distributed computing as well. Chess-playing machines and the like also belong to this category. Big data also shows up in this category – when interactively exploring data, you would like queries to run in reasonable time.