This is the 8139th most frequent Russian word.
летний
"Летний" means "summer" or "summery" in English.
In this sentence, 'летним' is an adjective describing the type of day, modifying 'днем' (day) and indicating that it occurs in summer.
Он наслаждался тёплым летним днем в парке.
He enjoyed the warm summer day in the park.
Here, 'летний' is used as an adjective to describe the palace and indicate its seasonal usage or association with summer.
Её летний дворец расположен на берегу реки.
Her summer palace is located on the riverbank.
In this example, 'летнюю' is an adjective modifying 'прогулку' (walk) to specify the nature or timing of the walk as related to summer.