The side that has been put in check must escape the king or use other methods to block it.
Literal
Check [object-を] put-[passive-られた] side [topic-は], king [object-を] escape [etc.-など] [possessive-の] method [with-で] check [object-を] must-block.
A shogi/chess rules explanation. 王手 (check) and 玉 (king piece in shogi) are game-specific terms. ~かけられた (was put on) uses the passive. 防がねばなりません is the literary must-form (~ねばならない being more formal than ~なければならない). ~など marks 'methods such as escaping.'