I'm a little confused about the cookie and I want to know can we use cookies somewhere other than the browser, like a mobile app or desktop app. Is the cookie dependent on the browser?
No, cookie is not dependent on browser.
Cookie is dependent on HTTP "User-Agent" -- the software/library client that is acting on behalf of a user, following HTTP protocol. Browser is just one type of it. Other types of "User-Agent" includes:
In a mobile app or desktop app, if HTTP is used for application, it is highly likely that cookie is used.