Midsummer Day vs Midsummer's Day

Midsummer Day and Midsummer's Day both are nouns.

Word	Noun	Adjective	Verb	Adverb
Midsummer Day	Yes	No	No	No
Midsummer's Day	Yes	No	No	No

As nouns, Midsummer Day and Midsummer's Day are synonyms defined as:

Midsummer Day and Midsummer's Day: a quarter day in England, Wales, and Ireland

Other synonyms of Midsummer Day include June 24, St John's Day.

Midsummer Day (noun)	Midsummer's Day (noun)
a quarter day in England, Wales, and Ireland	a quarter day in England, Wales, and Ireland