This is a counter for "one small animal" or "one insect." It is often used for pets like cats, dogs, or fish, and for smaller creatures. Note the pronunciation change from "ひき" to "ぴき" for one.

小(ちい)動物(どうぶつ)や昆(こん)虫(ちゅう)を「一(いっ)匹(ぴき)」数(かぞ)える助(じょ)数(すう)詞(し)。猫(ねこ)、犬(いぬ)、魚(さかな)などに使(つか)います。発(はつ)音(おん)は「いっぴき」です。