The History of Sugar Plums
Sugar plums are connected to Christmas in a few different ways.
Firstly they were a very popular candy/sweet from the 17th to the 19th centuries. They are mentioned in the poem 'A Visit from St Nicholas' ('Twas the Night Before Christmas') which says "The children were nestled all snug in their beds; While visions of sugar-plums danced in their heads;" and there's also The Sugar Plum Fairy in The Nutcracker Ballet.
Although they're called sugar plums, they don't contain plums! In the 1500s and 1600s the term 'plum' could refer to any kind of dried fruit, like raisins and currants, as well as plums (it could also mean other things which people thought were good to eat). In France candy/sweets like sugar plums were/are known as dragées and in Italian almond based candies like this are known as confetti di Sulmona.
Sugar plums were a kind of 'comfit', a kind of sweet/candy which was made from a small nut, seed to spice which was coated in many layers of sugar and edible gum like gum arabic.
To make them you start with the centre item, like an almond, pine nut or aniseed and they are rolled/tumbled/panned in multiple thin layers of the sugar syrup and gum mixtures. Towards the end of the process colors can be added to the sugar syrup.
In the 1700s sugar plums were often sold in paper cones. As sugar became cheaper, in the 1800s, sugar plums became a popular sweet/candy which most people could afford. Before this only rich people could afford to buy them.
In the Victorian period some medications, especially for worms(!), were sold as 'sugar plums' as the unpleasant medicine was coated in sugar, to help children take them.
The closest candy/sweet to sugar plums today are sugared/Jordan almonds. You could also say that M&M's are also a kind of dragée/sugar plum!
Although the Sugar Plum Fairy is a character in the ballet version of The Nutcracker, there's no fairy in the original story. However, there are sugar plums in the story, but they're used as cannon balls by the mouse army! (Sugar plums were a slang term used for cannon balls at this time.)