Sir Walter Elliot describes the appearance of an admiral he bumped into. As is usual with Sir Walter, the admiral's looks are the primary means by which he judges the man. In contrast to today's standards, tanned skin was then considered unattractive.
Here, in comparing him to mahogany, a wood ages by darkening, he is showing the current interest in things exotic. The mahogany he refers to most likely came from the West Indies, or the Bahamas.