How do PCR duplicates arise and why is it important to remove them for NGS analysis?
In any scenario where depth of coverage is an important factor, PCR duplicates erroneously inflate the coverage and, if not removed, can give the illusion of high confidence when it is not really there.

For example, consider the following hypothetical scenario.

                                         *
TTTCATACTAACTAGCCTGCGGTCTGTGTTTCCCGACTTCTGAGTCATGGGGTTTCAATGCCTATAGATTC
               ..........................C.
                ............................
                      .............T..............
                       ..................C.........
                           ............................
                               ............................
                                   ............................
                                    .....C......................
                                       ..C.........................


The marked position has a coverage of 9 (9 overlapping reads), 4 of which suggest the presence of an alternate allele. Since these 4 reads map to different positions, they are independent observations supporting the same putative single nucleotide variant (SNV). The T in the third read can safely be ignored as a sequencing error, since it only appears once.

Now consider the following hypothetical scenario.

                                         *
TTTCATACTAACTAGCCTGCGGTCTGTGTTTCCCGACTTCTGAGTCATGGGGTTTCAATGCCTATAGATTC
                ............................
                      .............T..............
                       ..................C.........
                       ..................C.........
                       ..................C.........
                       ..................C.........
                               ............................
                               ............................
                               ............................


In this case, the marked position also has a coverage of 9, but 7 of those reads appear to be PCR duplicates. If we remove the duplicates, the marked position has only a coverage of 4, and only one C at the marked position, which is not enough confidence to call the SNV.