If you mean a manager in the traditional "showbiz" sense, then a YouTube manager would be someone who helps manage the day-to-day operations of a YouTuber. Most likely only very successful YouTubers would need a manager, as there wouldn't be too much activity for a manager to handle for a "smaller" channel. A manager would potentially be the first point of contact for any business requests, they'd handle publicity/marketing opportunities (assuming the YouTuber doesn't have a specific PR person), help run a schedule for the YouTuber if they have a lot on their plate, broker deals with other industry professionals, etc. Most often than not, I believe even most "big" YouTubers are their own managers because, even when successful, it's not like they're a movie star being inundated with constant contact. If not, maybe they have a friend or family member that helps keep things in check for them. I'd imagine it's the very "top" YouTubers that would have actual professional managers that take a % cut of profit - i.e. YouTubers that have been successful enough to release a book, as they probably wouldn't be able to handle all that work alone.
This definition of "manager" is slightly separate from a show-biz one, as I believe a YouTube manager also takes on some of the responsibilities that a traditional talent agent would, but most YouTubers wouldn't need a talent agent unless they're specifically looking to branch out into film/music.