An elderly person; one who is past the age of retirement.
This American phrase was coined in the 1930s as a euphemism for 'old person' and has since spread to many other English-speaking countries. Prior to that the term 'senior citizen' had been used but was restricted to those people who were the oldest in their community; for example, this piece from the Canadian newspaper The Manitoba Free Press, October 1930:
"Today, friends of 'Dad' Quick, Vancouver's senior citizen, congratulated him on the attainment of his 110th birthday."
In 1938, several US newspapers reported the 'Thirty Thursday' plan by the Commonwealth Party's candidate for governor, Robert Noble:
"On Nov. 8, the people of California will vote on the scheme as a proposed amendment to the state constitution. If passed, the retirement life payment plan, as it is called, promises to pay $30 a week for life in state script to every "senior" citizen, man or woman, 50 years of age or over."
Fifty seems quite young to be considered 'senior'. The life expectancy in the USA in 1938 was 63 (in 2005 it was 77), which may account for that.
'Senior citizen' has largely replaced the previous 'old-age pensioner', which some considered derogatory (although I've never yet met an old person who objected to being called old).