In this sense I think it means the gifts or maybe decorations.
There are multiple definitions so i tried googling the definition:
Noun:
An ornamental festoon of flowers, fruit, and greenery: "ribbon-tied swags of flowers".
Verb:
Arrange in or decorate with a swag or swags of fabric.
Synonyms:
noun. loot - booty - spoil - prey - plunder
Usually these days if you hear the word it's in a hip-hop/pop music context like "check out my swag" and it's short for "swagger", as in "check out my cool style/self confident way of walking!"
I've also heard it at conferences when companies give out free stuff. "Look at all the swag I got from Microsoft!" That would be the "loot / plunder" synonyms given above.
However, I wasn't aware of the "festive decorations" definition and that's almost certainly what they're talking about if they say "Christmas Swag". My second guess would be presents as in the definition "loot/plunder".