artistic taste; aptitude for painting; ability to appreciate art
Refers to a person's innate sense for art, including both the ability to create and to appreciate visual art. Often used in phrases like 絵心がある (to have an artistic eye) or 絵心がない (to lack artistic sense).
He has an artistic eye and is very good at sketching.
I have no artistic sense, so even when I go to an art museum I don't really get it.
desire to paint
A less common nuance focusing on the urge or motivation to paint, rather than innate ability. Can be seen in contexts like 絵心が湧く (to feel like painting).
Seeing the beautiful scenery, I suddenly felt the urge to paint.
Compound of 絵 (e, 'picture, painting') and 心 (kokoro, 'heart, mind, spirit'), with rendaku voicing. The exact historical derivation is uncertain, but the combination naturally expresses an innate sense or feeling for art.