Amortization refers either to paying debt in regular installments over time or deducting intangible capital expenses over time.
When it refers to debt, amortization is the practice of spacing out payments on that debt at regular intervals. For example, a 30-year fixed-rate mortgage usually requires monthly payments on the debt.
In amortized loans, each monthly payment contributes to paying off both the principal and the interest being charged on that principal. Because the amount of principal remaining on the debt changes with every payment, the proportion of each payment that goes to interest is reduced with every payment. These changing proportions are described in an amortization schedule.
This is why contributing additional money towards a debt's principal significantly reduces the interest paid out over the life of the loan.
When amortization refers to capital expenditures, it describes the practice of accounting for intangible capital expenditures (such as intellectual property) over the life of the expense to reflect their consumption or expiration.
For example, a copyright that cost $10,000 and would run out five years hence would be amortized at $2,000 a year for each of those five years.