The keys are the keys to the Radio Tower. There was someone or something outside and Rousseau wanted to lock the door to keep them from getting inside.
Brennan took the keys before Rousseau killed him. It is only days later, after his death when she is recording her message at the Radio Tower that she realises than the keys are gone. She may've seen Brennan lurking around suspiciously in the Radio Tower earlier so when she sees that the keys are gone she knows who took them.