From what I understand, we outside of Eretz Yisrael we keep two days of Yom Tov as a continuation of the minhag that evolved from the time of the Bais Hamikdash when we would not necessarily know when Sanhedrin in Yerushalyim declared it to be Rosh Chodesh. In order to be sure that we keep Yom Tov on the correct day, we keep two days.
What I don't understand however, is why is this not the minhag in Eretz Yisrael? After all, just because you live in Eretz Yisrael today, it doesn't mean you are not technically in Golus. Also, there is no Sanhedrin in Eretz Yisrael today just as much as there is no Sanhedrin in Chutz L'Aretz today - meaning there is no central body anywhere to establish when Rosh Chodesh is.
According to all these educated assumptions, I can't see why Israelis would hold one day while British Jews, for example, keep two.
I would appreciate very much if someone could clarify.