A fixed interest rate is an interest rate which will not change for the life of the loan. Loans such as mortgages and car loans are often offered with fixed interest rates. There are advantages for both borrower and lender with such rates and they are extremely common.
With a fixed interest rate, when the loan is originated, a single interest rate is set and it will continue throughout the life of the loan until it is paid off. For example, someone could take out a car loan at 4.75% interest. Until the car was paid off, that person would pay 4.75% interest on the loan. The interest rate would not deviate.
For borrowers, one big advantage to a fixed interest rate is that the payments over the life of the loan can be calculated. The borrower knows that payments will remain consistent, can estimate how much will be paid over time, and can plan ahead. By contrast, if the rate is subject to change, the borrower's payment amounts can grow or shrink, and the loan can be more difficult to manage. For lenders, offering fixed interest ensures a steady supply of interest payments over the life of the loan.
When a fixed interest rate is determined, the lender usually does so by looking at the current discount rate, the rate charged by the central bank for loans taken out by financial institutions. If the discount rate is relatively high, the lender may offer a lower fixed interest rate under the argument that rates will drop in the future. If the rate is low, the assumption is that it will rise in the future, so the rate offered will be higher.
Borrowers are not necessarily frozen in a fixed interest rate forever. They can choose to refinance their loans and some may do this. If rates drop, a borrower with a high interest rate might opt to refinance at another lower rate. People with student loans can also opt to consolidate their loans and shift from a variable interest rate based on the prime rate to a fixed interest rate.
There can be caveats with a fixed interest rate which are important to be aware of. For example, some lenders may change the interest rate if a borrower defaults or makes late payments. This will be disclosed in the promissory note signed at the time the loan is taken out.