I know that there are some Pagan origins of Christmas, but what exactly are they?
There are no Pagan origins of Christmas. Very simple.
There are ancient European Pagan festivals that were celebrated at mid Winter, such as Yule among the Germanic folk, Saturnalia and Sol Invictus among the Romans. The Romans halted normal business at Saturnalia and turned to feasting, singing, merriment and gift giving. (Sound familiar?) Yule seems to have been connected with the Wild Hunt and Mothersnight. Certainly the practices of burning a Yule log and the sacrifice of the Yule boar as still with us (in the form of roasting chestnuts over a merry Christmas fire and eating ham on Christmas!).
Some of the practices of the European Pagans have indeed been imported and sanctified by Christianity, but that's the limit of their connexion with Christmas.
The origins of Christmas per se, quite simply, is the historical occasion of the birth of the God-man, Jesus.