I tried looking for other readings (like soure), but I didn't see anything. Going only by the Romaji, then sore means "that." "Kore" is "this" and "are" is "that (whatever) over there."
Combined with other prepositions, particles, and what not...
sorekara= as a result, thus, therefore
sore wa (or) ga = that is (as in "that is a car")
sorenara = if that were true, if that came to be

So here's a few ideas. Good luck.
There's a good technical dictionary site listed below if you're interested.

"sore" is used when the object that you are talking about is closer to the person you are talking to. You would use "kore" if the object is closest to you and "are" if it isn't close to any of you.