In a southeasterly direction means moving or facing toward the southeast.
Southeasterly can make people think of warm places or of the ocean.
Examples:
The wind is blowing in a southeasterly direction.
We need to go in a southeasterly direction to get to the beach.
The birds are flying in a southeasterly direction for the winter.
I always feel warm when the wind is southeasterly.
The treasure is buried in the southeasterly part of the island.
The boat sails southeasterly toward the warm sun.