dancer; dance artist
Refers to a professional dancer or a person accomplished in dance, often in traditional or artistic contexts. The glosses 'dancing master/mistress' are older or more formal terms; the core meaning is a dancer as an artist.
She is a famous dancer.
その舞踊家は古典バレエを専門にしている。
That dancer specializes in classical ballet.
Compound of 舞踊 (buyō, 'dance') and 家 (ka, 'person, specialist'). The exact historical derivation is straightforward; 舞踊 itself is a combination of 舞 (bu, 'dance') and 踊 (yō, 'dance').