What does paired-end sequencing add over single-read sequencing?

Why

In single-read sequencing, one end of each fragment is read. In paired-end sequencing, both ends are read, and the two reads are known to come from one fragment of roughly known length, facing each other. Illumina's own guidance lists the gains: more accurate alignment, better handling of repetitive sequence, and easier detection of insertions, deletions, inversions, gene fusions and novel transcripts.

The logic is that one read may fall in a repeat and map to many places, while its mate lands in unique sequence and anchors the pair. A pair that maps too far apart, in the wrong orientation or on two chromosomes is evidence of a structural change. The known pairing also helps duplicate marking, because two pairs with the same start positions for both reads are much more likely to be PCR copies than two single reads that share one start.

Single reads remain adequate and cheaper for counting applications, such as many gene expression or ChIP-seq studies, where the question is how many reads fall in a region rather than its exact structure.