It's like the bar code on a security. You need long hairy numbers to be assigned to each security to prevent confusion. Many stocks have multiple flavors - some have higher voting rights or other non-economic interests attached to them. Others have ADRs or non-US elements. For many bonds, there are a dozen or more series, many of which have barely discernable differences in terms and having a unique CUSIP allows for the securities to be individually identified so when you thought you were buying a cow, you actually got a cow and not a bunch of magic beans.