na-adjective, noun which may take the genitive case particle 'no'
large-pupiled; dark-eyed; having large irises
Describes eyes where the dark part (iris/pupil) appears large or prominent, often giving a cute or striking impression. Used for people, dolls, or characters.
彼女は黒目がちな大きな目をしている。
She has large, dark eyes with prominent pupils.
その人形は黒目がちで愛らしい顔をしている。
That doll has a cute face with large dark eyes.
黒目 is the dark part of the eye (iris/pupil), while 黒目がち describes the quality of having large or prominent dark parts.
Compound of 黒目 (dark part of the eye) + がち (tendency/predominance). The exact historical derivation is uncertain, but the meaning is transparent from its components.