The phrase 'No Spring Chicken' is usually used in a negative way to describe someone who is no longer young, probably past his young adulthood, and sometimes doesn't realize it and tries to look and act younger than his age.
Example of use: "I don't know how old Mike is, but obviously he is no spring chicken."
The origin of the phrase actually comes from its literal meaning. In the early 1700s, Farmers found that chickens born in the spring brought better prices than 'old' ones that had gone through the winter. When farmers tried to sell the old birds as 'new spring born', buyers complained that they were 'no spring chicken'. The first recorded use of the phrase in its figurative meaning was in 1906.