What is Hard drive rpm?

Rotations per Minute. It's the rate at which the platters spin. Most "standard" desktop drives spin at 7200rpm, which means the disks rotate about 120 times every second.

You will find hard drives at 4,500, 5,400, 7,200, 10,000, and I think even 15,000 rpm.

The faster the platters spin the higher the theoretical performance. For one thing if you try to read some data and what you want to read is halfway around the platter at that instance, it will take 1/2 rotation before your data gets to the read/write head. With faster platter rotation the read/write head will be able to get it faster. For the other thing the faster the platters rotate the more data the read/write head will be able to read in any given time, which ups the transfer rate.

Think of it like this- if your table top was round and you covered it with cake frosting, then somehow made it rotate, the faster it rotates the faster you can scoop up the frosting if you hold a spoon against the top of the rotating table.