To amortize a loan usually means establishing a series of equal monthly payments that will provide the lender with 1) interest based on each month's unpaid principal balance, and 2) principal repayments that will cause the unpaid principal balance to be zero at the end of the loan. While the amount of each monthly payment is identical, the interest component of each payment will be decreasing and the principal component of each payment will be increasing during the life of the loan.
To illustrate, let's assume a lender proposes to amortize a $60,000 loan at 4% annual interest over a 3-year period. This will require 36 monthly payments of $1,771.44 each. The first payment will consist of an interest payment of $200.00 ($60,000 X 4% X 1/12) plus a principal payment of $1,571.44 ($1,771.44 - $200.00). After the first payment is made, the principal balance will be $58,428.56 ($60,000.00 - $1,571.44). The second monthly payment of $1,771.44 will consist of interest of $194.76 ($58,428.56 X 4% X 1/12) plus a principal payment of $1,576.68 ($1,771.44 - $194.76). After the second payment is made, the remaining (or unpaid) principal balance will be $56,851.88.
The 36th and final monthly payment of $1,771.44 will consist of interest of $5.89 (the principal balance after the 35th payment, which will be $1,765.55, times 4% X 1/12) plus a principal payment of $1,765.55. After the 36th payment the loan balance will be zero. In other words, the loan will have been amortized over its 3-year term.
A listing of each month's interest and principal payments (and the remaining, unpaid principal balance after each payment) is referred to as an amortization schedule.