Cats age much faster than we do. Some people believe that cats live about 7 cat years for every one year of our life. It's a little more complicated than that and may be closer to 5 cat years to our one year.
Most cats are considered senior in the last 25% of their lives. If a healthy indoor cat lives to be 18 years old, he or she would be considered to be senior around age 13.
For more information on keeping your senior cat healthy, read Keeping Your Senior Cat Healthy