A public (or paper) petition is a petition to the House of Commons presented by an MP. E-petitions enable members of the public to petition the House of Commons and press for action from the Government or the House of Commons.
Groups or organisations can petition Parliament against a proposed Private Bill. Private Bills only change the law as it applies to specific individuals or organisations, rather than the general public.
A member of the House of Lords may also present a petition to the House of Lords reading out who the petition is from and what action the petitioner(s) wish the House to take.