In abundance; very much.
It's easy to believe that this expression derives from the imagery of digging with spades and that 'in spades' is just short for 'in spadefuls'. However, the spades concerned here aren't the garden tools but the suit of cards. Spades is the highest ranking suits in the game of Contract Bridge, a very popular pastime in the USA in the early 20th century, which is when and where the phrase originated.
Despite the agricultural-sounding name and the shovel-like shape, the suit in cards has nothing directly to do with garden spades. Playing Cards originated in Asia and spread across Europe around the 14th century, arriving in England a little later than in Spain, Italy and Germany.
The Italian versions of early cards used the suits Cups, Swords, Coins and Batons, which, on migration to England, became Hearts, Spades, Diamonds and Clubs. The image for Spades on English and French cards looks somewhat like that of the German Acorn or Leaf suits, but its origin is revealed by its name rather than its shape. The Spanish and Italian for sword is 'espada' and 'spada' respectively, hence the suit 'Swords' became anglicized as 'Spades'.
We have been 'calling a spade a spade' for many centuries, but the expression 'in spades' is a 20th century US coinage. The term was often used before that in relation to card games, where Bridge contracts might be entered into in the minor suits of Clubs or Diamonds or, for the higher scores, 'in Hearts' or, best of all, 'in Spades'.
The figurative meaning, i.e. the non-cards-related 'very greatly' meaning, isn't found before the 1920s. The American journalist and writer Damon Runyon used the expression that way in a piece for Hearst's International magazine, in October 1929:
"I always hear the same thing about every bum on Broadway, male and female, including some I know are bums, in spades, right from taw."
It isn't possible to be sure that the figurative 'in spades' derives from Bridge, but the coincidence of the time and place of the origin of the expression and the popularity of the card game certainly does suggest a connection.
See also: Grand Slam.
See other phrases that were coined in the USA.