- The timing; Saturnalia was not on exactly the same date as Christmas, but it was in late December (17th-23rd) which is close enough.
- The food; Saturnalia was celebrated with lots of eating and drinking, just like Christmas is today (at least in my family).
- The presents; Romans gave each other small gifts at the time of the festival. The poet Martial mentions as presents a pig, a parrot, dice, knuckle bones, moneyboxes, combs, toothpicks, a hat, a hunting knife, an axe, lamps, balls, perfumes, pipes, a sausage, tables, cups, spoons, items of clothing, statues, masks, and books (among other things).
But what characterised Saturnalia most of all was the role reversal of slave and free. Freeborn Romans would wear the pileus- a hat usually only worn by freedmen, and slaves would recline at luxurious banquets, waited upon by their masters. During this time slaves were also permitted to gamble, and could not be punished by their masters. It was a time of general relaxation, enjoyment and hilarity, much enjoyed by the Roman people- Catullus calls Saturnalia the best of days (die... optimo dierum) and attempts by the emperors Augustus and Caligula to shorten the celebrations failed, due to overwhelming popular support.
December est mensis: cum maxime civitas sudat. ius luxuriae publice datum est; ingenti apparatu sonant omnia, tamquam quicquam inter Saturnalia intersit et dies rerum agendarum.
It is now the month of December, when the whole city sweats. The right of luxury is given to all people; everywhere you can hear the sound of great preparations, as if there were some real difference between the days devoted to Saturn and those for doing normal business.
(Epistulae Morales II.XVIII)
inter haec servilis moderator obsequii ammonet dominum familiam pro sollemnitate annui moris epulatam. hoc enim festo religiosae domus prius famulos instructis tamquam ad usum domini dapibus honorant: et ita demum patribus familias mensae apparatus novatur.
Meanwhile the head of the slave household came to tell his master that the household had feasted according to the annual ritual custom. For at this festival, in houses that keep to proper religious usage, they first of all honour the slaves with a dinner prepared as if for the master; and only afterwards is the table set again for the head of the household.