microRNAs are very short (about 25 nucleotides) they are never translated into protein, instead they form stem-loop structures. They are thought to control the expression of other genes... they bind to complementary sequences in normal messenger RNA and target them for degradation.
RNAi basically utilizes this endogenous pathway... it is a technique for silencing the expression of target genes.
These are the very basics, but obviously the mechansms by which they occur are detailed. Ambion.com has a very good explanation of RNAi becaus ehtey sell a lot of products for doing it.