Manga is chiefly categorized by audience first, then genre. This page will simply cover the four types of audiences to which manga are marketed. If you are looking for more information on manga genres and sub-genres, then check out: Beginner's Guide to Manga 3: Genres and Subgenres.
Shonen
Shonen often features lots of action, comedy, and some coming-of-age camaraderie between characters. Examples include Naruto, Fullmetal Alchemist, My Hero Academia, & The Promised Neverland.
Shojo
The focus here is less on the action and more on drama, emotion, and, almost always, idealized romance. Like shonen manga, shojo manga usually features the coming-of-age story of a young protagonist. You can usually identify shojo covers by their use of pretty pinks, flowers, or other cutesy images. Examples include Sailor Moon, Fruits Basket, and Skip Beat!