RNAi is the complementary strand to a RNA molecule which normally would be translated into a protein. The RNAi molecules do normally not exist because only one strand of the DNA is translated.
But if you have a complementary strand to an RNA molecule it can do exactly what a DNA strand would do with its complementary strand – they bind together.
Double stranded RNA can not be translated, so no protein the original RNA is coding for is produced.
RNAi is used to eliminate the production of one specific protein in order to study its function.
The nice thing about it is, that using standard genetic engineering methods you can let RNIi only be produced under certain conditions (e.g. heatshock), so you can switch the protein on and off either under certain conditions and even only in certain cells (depends what promotor you use).

RNAi is basically a small RNA molecule which inhibits protein translation. It lowers the level of specific proteins in cells. Why? Because if you block translation but protein degradation continues, then the protein gets degraded. The mechanism of inhibition of translation is due to interaction with the RISC complex. The mechanism is actually quite complex and beyond high school or college biology. Here is a review looking at RNAi. You can look for other literature or even at company websites to get basic info on RNAi.