For mention is basically the court finding out if something is going ahead or not, the registrar calls it and the lawyer/s or the party themselves (if they are not represented) will tell the court to put it in the list or strike it out.
A motion is an application to the court for an order telling someone or something to be done eg produce documents (Discovery).
The Defendants are bringing a motion to stay proceedings - possibly to arbitration (see section 5 of the arbitration act 1980). No papers means that the applicant has not lodged any papers with the court in advance (not usually required if its just for mention).