Seikon no Qwaser II Things

Abbreviation of Big Freakin' Sword (and it's less polite wording). Insanely big and heavy swords which sometimes weigh more than the character himself/herself. Generally they're also magical.

A Bokken is a wooden sword that is used for training. It is normally the same size and shape of a katana.

A mask is an object worn to cover the face. They can be just small enough to cover the eyes or the entire face. A person normally wears a mask to attempt to hide their identity.

The character is wearing school uniform. Most probably he/she's a student.