Depreciation, refers to prorating a tangible asset's cost over that asset's life. For example, an office building can be used for many years before it becomes run down and is sold. The cost of the building is spread out over the predicted life of the building, with a portion of the cost being expensed each accounting year.
Amortization usually refers to spreading an intangible asset's cost over that asset's useful life. For example, a patent on a piece of medical equipment usually has a life of 17 years. The cost involved with creating the medical equipment is spread out over the life of the patent, with each portion being recorded as an expense on the company's income statement.