This is the 4807th most frequent Russian word.
знакомую
"Знакомую" means "a (female) acquaintance."
Here, "знакомую" (accusative form) is used to refer to a female acquaintance that the speaker met, appropriately contextualized with the verb "встретил" (met).
Я встретил знакомую в магазине вчера.
I met an acquaintance at the store yesterday.
In this sentence, "знакомую" again signifies a female acquaintance, fitting the context of being introduced by a friend.
Моя подруга познакомила меня с своей знакомой.
My friend introduced me to her acquaintance.
"знакомую" here appears in the context of being mentioned or described by another person, with proper grammatical alignment to the prepositional phrase "о своей знакомой".