A hen is a female chicken, while a chicken can refer to either a male or a female of the species Gallus gallus domesticus. "Hen" can also be used to refer to a female bird of any species.
Both the words "hen" and "chicken" also have further colloquial meanings. For example, Merriam-Webster notes that "chicken" can also refer to a young woman, petty details, a coward or a homosexual man. It can also, of course, refer to the flesh of the chicken. "Hen" sometimes also names the females of certain aquatic species, such as lobsters, and it can also refer to a woman, especially a fussy, middle-aged one.