Meaning: This sentence describes a group of children who were running after each other in a playful manner.
Choice of Words: The word "they" is a pronoun that refers to a group of people. "Chased" is a past tense verb that means to pursue or try to catch someone. "Each" is a pronoun that refers to one of a group of people or things. "Other" is a pronoun that refers to the second of two people or things. "Around" is a preposition that means in or near a place. "The" is a definite article that refers to a specific thing. "Playground" is a noun that refers to an area where children play.