The K-On! girls are going to London and Yui wants to practise English so instead of calling Azusa “Azu-nyan“, she calls her “Azu-cat“. Later the other girls use this as a play on words.
It comes from the Japanese words “預けて“ (azukete) which means “to entrust“ and “預かって“ (azukatte) which means “to take care of“.
軽音部たちはロンドンへ行く。唯は英語を練習したいから、梓が「あずにゃん」と呼ばなくて、「あずキャット」と呼ぶ。あとで、ほかの3人は駄洒落にこれを使う。