"White Russia" is actually the English translation of Belarus! So that is what that means.
Belarus is immediately to the east of present-day Poland, which until the end of WWII, had borders a couple of hundred miles east of where they are now in 2015. Byelorussians are ethnically Slavic, and stand midway between Russians and Poles in the Slavic ethnic tree, and would also be closely-related to Ukrainians. Byelorussia (it's self-appellation today) was not actually a political nation until 1991. It was one of the 16 Soviet Republics of the USSR though. The territory of this ethnicity was part of Russia until then, though the borders were moved after WWII as I mentioned. Byelorussian is a seperate language, probably close both to Russian and to Polish.
I think your Polish family has given you as good a start as you could get. English sources on this area are few and far between, so you had better brush up on that Polish, and read up on the histories of the nations listed above. You should try to establish what city or area your Belarus great-grandfather is from (by asking your Polish family), and go from there. Good luck!