This is an old folksong and the written version of the text first appeared in 1850 in a Danish paper, sligthly different from the version we are singing today:
Jólasveinar ganga um gólf með gildan (gylltan) staf í hendi.
Móðir þeirra sópar gólf og flengir þá með vendi.
Uppá stól stendur mín kanna, níu nóttum fyrir jól þá kem ég til manna.
It is not easy to translate the text but it would be something like this:
Yule lads walking the floors with a broad (or golden) walking stick in their hands. Their mother is sweeping the floor and spanking them with a wand. Upon the chair is my cup, nine night before Christmas I come to the village.