The prime interest rate, or prime rate, is the interest rate for debt that has a high potential for payback and is low risk to the lender. Based on your credit history and employment, a lender or credit card institution will decide where you fall into the interest rate hierarchy. Banks, credit card companies, and lenders will demand a higher interest rate if your credit history indicates you as a "subprime" borrower with higher risk, simple enough.
These rates and practices are an important part of the vicious cycle that many credit card victims fall into. As debtors get stretched thinner, many are tempted to take out more credit cards and pay off bills with other credit cards, etc. This creates a magnification of the debt, essentially transferring payments to higher and higher interest rates as the individual's credit rating deteriorates. Scrambling to take out another credit card while already struggling creates an impending disaster as the terms become more restricting. People in this cycle are often hit with fees (addressed by CARD Act) and it is important to be aware that interest is not the only thing you need to worry about.
An additional layer of danger is added by adjustable interest rates. These variable interest rates will surge when payments are missed, effectively locking a credit card customer into debt. These type of rates were addressed by the CARD Act, and have been restricted since they were so destructive.
It is critical to be wary of this debt cycle and the dangers of deferring payments for perceived convenience. Understanding the true consequences of falling into this trap will hopefully serve as a strong deterrent from irresponsible spending.