Be logged in; go to your account settings or simply use the link. All contributions will be gone and that's probably what you wanted too.
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks: this can be found mostly in the Terms of Service/Privacy Policy; otherwise you can always contact CloudApp and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for CloudApp using a third-party login such as Facebook or Twitter, you probably want to revoke all access from CloudApp. Click the icon below to find out how.