The only personal information ApriBot stores about you is your Reddit username (on posts which you have labelled). This information is required to make sure that you are not asked to label the same post twice. It is not shared with anybody else, and your votes can only be viewed by you.
ApriBot uses one cookie to log you into Reddit securely (using OAuth), and another to store your login status so that you don't have to keep logging in, but otherwise does not perform any other tracking. If you want to verify this, the source code of ApriBot can be viewed on GitHub.