If you are working for an organization and you say that you feel like a square peg in a round hole, what you mean is that you feel like a total misfit. You and the others around you sense that you do not belong there.
This expression can be used to refer to refer to someone who is unsuited for the type of job he/she is actually doing.
I have always felt like a square peg in a round hole in this school.
He felt like a square peg in round hole in this office. Thus he resigned from his post.