A cat in the old days was not just a pampered pet as they often are today, but a hard working, practical member of a household.
Cats and humans had made a partnership contract with each other ages before--in exchange for living quarters and an occasional meal, a cat would keep your house free of pesky vermin--notably rats and mice--which always were a nuisance.
Of course Dick Whittington's cat knew and understood this contract so beside being a fun companion to the little boy, the cat did his traditional job and kept the big house free of rats and mice. In fact Dick Whittington's cat became notable for his "mousing" ability.
Mr. Fitzwarren, Dick's kindly protector, was, as we have said, a rich and powerful merchant.
This means he bought and sold many things--and his business was in the shipping trade.
He probably owned several ships and would hire captains and crews to sail his ships to distant lands where they would trade the things made in London for other things the Londoners wanted to buy--maybe spices from the Spice Islands or cocoanuts from the South Pacific or beautiful porcelain and silk from China-- because London was a good market for all kinds of foreign things.
One day, Mr. Fitzwarren asked young Dick, who had grown into a likely lad, if he had anything he would like to send with one of his ships that was preparing to sail to a far-away land to trade for things to sell in London.
But Dick had nothing at all to trade.
"Well, my lad, why not send your cat?" suggested Mr Fitzwarren. "Who knows but what some oriental potentate would not like to have such a pretty and practical animal around and might trade you something valuable for it."
And though Dick didn't like to lose his friendly cat--he also considered that this might be his only opportunity to start his own fortune--so he agreed.
The ship captain was also happy to have the good mouser aboard to keep his ship clear of pesky rodents on the long voyage out--and so the deal was done.