1. What does it mean?
따아 is short for 따뜻한 아메리카노. It contrasts with 아아, the shortened name for an iced Americano.
Also written or said as 따뜻한 아메리카노, hot americano
2. The nuance
It describes the temperature and drink type, not the strength of the coffee. The abbreviation is convenient among people familiar with it; saying 따뜻한 아메리카노 주세요 is clearer when placing an order that might otherwise be misunderstood.
3. Examples
“오늘은 목이 차가운 게 싫어서 따아로 골랐어.”
I didn't feel like having a cold drink today, so I chose a hot Americano.
“따아 한 잔이랑 우유 없는 차 한 잔 부탁해요.”
One hot Americano and one tea without milk, please.
Sources
KoreanClass101: Korean language lessons
References support the meaning and usage. Example sentences are written for NoCapWiki.