It's an interesting and very pertinent question!
In Jewish tradition the calendar is determined by eyewitness sightings of the full moon, and then declared by the Jewish Supreme Court, the Sanhedrin in Jerusalem. In the days of the Temple people outside of Israel simply would not know if the previous month was twenty nine or thirty days, and therefore would be in doubt as to which is the correct night when Succot begins, and when they must live in the succah - and likewise for other Festivals. Since it took more than two weeks to get to the Diaspora from Jerusalem, messengers would not arrive in time for the Festival, and the Diaspora Jews would have to keep two days of Yom Tov (Festival Days) due to doubt.
Nowadays we calculate the months based on a fixed calendar, but nevertheless the Sages of the Talmud decreed that outside of Israel Festivals still be kept as they were in ancient times as two days. So today in Israel the community keeps only one day of Yom Tov, whereas outside of Israel has two. The reason for the decree is just in case calculations and communications collapse for some unforeseen reason. The observance of a second day in such a case will be "playing it safe". It also mainly to maintain outside of Israel a feeling of connection and dependence of the "word of God coming from Zion and Jerusalem".
The most obvious way of removing the problem altogether is if the Jewish People can collectively bring about the coming of the Messiah, since at that point all Jewish communities will be brought to Israel and will all keep only one day. May it happen speedily in our days!
