If something is permissible, then it is allowed. If it's not permissible then you probably shouldn't be doing it.
If someone asked you, "Is it permissible for me to have a cupcake?" they're asking very formally for your permission to dig in. Usually the word permissible has to do with laws, rules, and what's generally acceptable. It's not permissible to take your pants off in public, for example. Wearing a hat inside is permissible according to the law, but it's not permissible according to church customs or your grandma's rules.