There are a few operations you can only do with DI/SI (or their extended counterparts, if you didn’t learn ASM in 1985). Among these are
REP STOSB REP MOVSB REP SCASB
Which are, respectively, operations for repeated (= mass) storing, loading and scanning. What you do is you set up SI and/or DI to point at one or both operands, perhaps put a count in CX and then let ‘er rip. These are operations that work on a bunch of bytes at a time, and they kind of put the CPU in automatic. Because you’re not explicitly coding loops, they do their thing more efficiently (usually) than a hand-coded loop.
Just in case you’re wondering: Depending on how you set the operation up, repeated storing can be something simple like punching the value 0 into a large contiguous block of memory; MOVSB is used, I think, to copy data from one buffer (well, any bunch of bytes) to another; and SCASB is used to look for a byte that matches some search criterion (I’m not sure if it’s only searching on equality, or what – you can look it up 🙂 )
That’s most of what those regs are for.