Nautilus's lore works greatly with his kit.
He is basically a hulking mass of sorrow. He is no longer who he once was, he is but a mere shell of his former shelf, a very strong shell. His kit is very symbolic of what he truly wants. Wanting to take people down to the depths with him.
His Q pulls them into him, dragging them down into the depths alongside him. While his W projects the wrath that he wishes to unleash on his enemies. His passive snares the enemy into the ground, while his E slows them preventing them from getting away. And finally his ult sends a wave knocking the enemy up into the air and stunning them so that they will not resist and join him in the depths.
Nautilus will pull his enemies down into the depths with him, so that they too know what it is like to be left behind.
TLDR: "Drag them down" - Nautilus