A colloquial term for the male genitalia, often used in humorous or euphemistic contexts. It refers to the physical organ and can also imply a sense of ownership or personal identity related to masculinity.
I would have to think it's because the unicorn stuffed animal is soft and plush and Deadpool's eyelids are one of the most sensitive parts on his body, so lightly rubbing your eyelids across the toy while masturbating was done so that he would trick his mind in thinking that the soft pleasing sensation was from the friction from his hand and his 'member'.