Moving or facing towards the southwest direction.
Moving southwestwards can be a good thing if you want to go that way.
Examples:
The bird flew southwestwards to find a warm place.
We walked southwestwards to reach the beach.
She pointed southwestwards and said the treasure was there.
The cat ran southwestwards to chase the butterfly.
The river flows southwestwards, making beautiful curves.
The wind blew southwestwards, carrying the scent of flowers.