In Japanese, -kei ～系 means "class" in what's probably the hardest to understand way possible. It's better translated as "type," "sort," "kind," or even "category." It's a suffix, going after whatever sort of sort you're talking about.
Although complicated to understand literally, the way kei 系 is generally used is to what "kind" of thing you like. For example, nichijou 日常 means "daily life." So nichijou-kei 日常系 means "daily life kind." A nichijou-kei anime is a slice of life anime, an anime categorized by dealing with the daily lives of characters, their nichijou.
The term "visual-kei band," or vijuaru-kei bando ヴィジュアル系バンド, is band classified by their focus on the visual: clothes, style, etc. rather than their music.
The terms nikushoku-kei 肉食系 and soushoku-kei 草食系 are "carnivore-class" and "herbivore-class," but it doesn't refer to animals, those are romantic personality types based on carnivores and herbivores, predators and preys. Although gender-less terms, the former generally refers to a girl who assertively goes after guys, and the latter generally a guy that's too timid to go after girls.
The word gyaru-kei ギャル系 would be literally "gal-class." This gal, gyaru ギャル, is a kind of look. So we can assume gyaru-kei refers to clothes "classified as gal," clothes a gyaru wears, that makes you look like a gyaru, of the gyaru kind, and so on. Sumber https://japanese-with-anime.blogspot.com/
