The most likely connotation of the word relaxing in the sentence is:
C. Tranquil.
When the speaker says: "I'm looking forward to a relaxing afternoon by the pool", he means he can't wait to spend a few hours by the pool without any source of stress or disturbance.
Other possible connotations would be: serene, placid, peaceful and calm.
Gabe was back at the Nurturing Center today, being cared for by the night crew. He had been given an unusual and special reprieve from the committee, and granted an additional year of nurturing before his Naming and Placement.
