"He is rear admiral of the white. He was in the Trafalgar action, and has been in the East Indies since;"
Trafalgar Battle
Public DomainTrafalgar Battle - Credit: Nicholas Pocock

 

Thus Anne Elliot describes Admiral Croft, the brother-in-law of her erstwhile fiance, to her father, who remains ignorant of most things naval.

Rear admiral is the lowest designation of the highest office in the Royal Navy (admiral).  The designation rear admiral of the white means that he is not in the lowest rank of rear admiral, but the middle.

The Trafalgar Action refers to the Battle of Trafalgar against Napoleon in 1805, where he would have been under the command of Horatio Nelson, who reached the rank of Vice Admiral of the White. 

The Nelson Society

Some of his letters, etc.

 

The East Indies, a long way from the West Indies where Captain Wentworth had such luck with the Asp, were made up of the islands of what is now referred to as Southeast Asia, including the Philippines and Singapore.

 

Map of the East Indies
Public DomainMap of the East Indies - Credit: William Dampier