When you increase the ISO you increase the signal output from the sensor, and that includes the noise from the electric charge running through it.
Here's an analogy: For a P&S with its tiny sensor it's like trying to push massive sound (lots of megapixels) through a tiny speaker (small sensor). The result will not be very clean. The smaller the speaker the more pronounced to undesired noise will be
_________________
Canon DSLRs: 5D Mark III, 7D
Canon lenses: 17-40/4
L, 24-105/4
L, 24/1.4
L II, 50/1.4, 85/1.8, 100/2.8
L Macro, 70-200/2.8
L IS, 100-400
LOther stuff: Canon 580 EX II, Canon 430EX II, Velbon Sherpa 600R
Apple: MacBook Pro 15", iMac 27", iPad III, iPhone 4S, Apple TV
My deviantART