Self-insertion is the act of putting a character in a story that resembles the author, called a self-insert. Self-inserts will usually:

• Look like the author (or look like how the author wishes he or she looked).
• Have hobbies similar to those of the author.*
• Have a name identical or similar to the author's.
• Share ethics and beliefs with the author.

*This generally doesn't apply when there are only one or two shared hobbies, or if the hobby is something that a lot of people have, such as reading, drawing, playing football, or playing video games. Also, if the hobby is "writing", then it definitely should not apply. After all, the person who writes about a writer has to be a writer.

Self-inserts are usually associated with Mary Sues, and while some are (Bella Swan for instance) some may not be. After all, no real human is a Mary Sue, so if you actually put yourself into the story, with all your flaws in place, you might have a good character.

The problem with self-inserts is that they often become what is known as an “Author’s Darling”. The author feels that the character really is them, and thus doesn’t let anything bad happen to them. Characters like this usually go through the story without so much as a scratch (physically or emotionally), and always accomplish all their goals (beat the baddie, win the contest, get the girl) in the end, without really having done much to earn it. Not a good story.

Now, nothing is wrong with giving a character the same hair color, your love of drawing, or the same sexual orientation as you. Don't feel is through you can't write a character who likes to draw because you like to draw too. Think of self-insert traits like the Mary Sue traits. A few are okay, just don't go overboard.