Avatar in Hinduism is a Sanskrit word meaning “descent”—The deliberate descent of a deity to Earth. The concept of an avatar is somewhat confusing, and a little complicated—much of Hindu mythology is. The concept is foreign to most cultures, as it is only prevalent in Hinduism and Sikhism. In Sikhism, the definition of an avatar is slightly different—instead of being the deliberate descent of a deity to Earth, it is the deliberate descent of a soul to Earth.
In all mythologies deities have some kind of form, or sometimes take some kind of disguise—avatars are unique though. They are entirely separate entities. For instance, the goddess Devi was a benevolent mother goddess, but her avatar Durga could be dark and destructive. Another way they can differ is in appearance. For instance, Vishnu was typically depicted as being mostly human-shaped, but blue and with four arms. But, one of his avatars is Matsya, who takes the form of a fish.
This is where things can get pretty crazy. Not only are there avatars, but then they are categorized into different groups of avatar ‘types’, which all have several sub-groups as well. Don’t worry about boggling your mind with all the specifics, it’s nearly impossible to memorize or recall all the avatars, especially of Vishnu.
Vishnu has a very large amount of avatars, some texts record up to 40, others 24, and other mention even more. The main three are the Trimurti: Vishnu, Shiva, and Brahma. The Dashavatara (a Sanskrit compound work meaning ‘ten avatars’) is the term for Vishnu’s ten best known avatars. There are also direct, and indirect avatars, and lots of others sub-categories.
Vishnu isn’t the only god to have avatars too (although, he perhaps has the most). Ganesha and Krishna also have avatars. Even avatars, like Shiva and Brahma, have avatars.
This can sometimes make Hindu mythology very confusing, but if you really want to learn about it all you have to do is understand the basic concept—that an avatar is an entirely separate form of the same deity (for instance, worshiping any avatar of Vishnu is the same as worshiping Vishnu)—and it will make this rather unique and somewhat puzzling concept a lot easier to grasp.