If you're an Orthodox Christian, you're definitely aware that you often celebrate Pascha (Easter) on a different day than most of your friends. If you're Protestant or Catholic, you may not know this, but your Eastern Orthodox friends often celebrate Easter on a different day. If you're Christian, you understand the resurrection of Christ to be the most important thing that has ever happened in the history of the world. Wouldn't it be nice to celebrate this event all together?
So why do the Eastern Orthodox celebrate Pascha (Easter) on a different day than the West.
In short, during the first few centuries there were disputes on when Pascha should be celebrated. The First Council of Nicaea in 325 determined that it was important for all churches to celebrate this “Feast of Feasts” together on the same day. What's ironic is, this feast seems to be the one that we don't celebrate together (we'll get to that).
First, it wasn't about being right. It wasn't about making sure it was on the exact day that it took place centuries earlier. It was about following a pattern in congruence with church practice. So we can stop arguing right now about who's more accurate or who's right or wrong.
At the council, they decided that it would always be on a Sunday. Further it would come after the first full moon after the vernal equinox.
Pascha Equation: First Sunday after first full moon* after Vernal Equinox.
This is still the equation for both the East and the West. So what’s the problem? The problem is the set day of the equinox and the calendar. First, depending on various calculations, the equinox could move, so the Church gave a set date for the equinox, March 21st. All celebrated together until it was realized that the calendar was becoming inaccurate and in 1582, Pope Gregory XIII of the Catholic Church introduced a more accurate calendar which included leap days every four years. Also to correct the issue, the calendar jumped 11 days in September of 1750 (I would not have had a birthday that year). The East did not accept this calendar and remained on the Julian calendar (named after Julius Caesar). At the present time, the Julian Calendar is now 13 days off. As a result, March 21st on the Julian Calendar is equal to April 3rd on the Gregorian (what we use in the USA). If a full moon happens between March 22nd and April 3rd then our Easters are not together. If the first full moon* after the equinox happens after April 3rd, our Easters are together.
*Note: To complicate things further, the full moon refers to a “Paschal full moon” based on a different equation. This might happen 2-5 days after an observed astronomical full moon (used by the West). This could cause a week difference if the full moon happens after April 3rd, as was the case most recently in 2015.
**Also Note: The biggest problem with this calendar change that some contest is that for there to be a major change in the liturgical life of the Church, which includes when we liturgically celebrate feasts, it needs to be a conciliar decision. Much of the issues the East has with the West is the primacy of the Pope, in that, the Pope can make such decisions regarding the church without a council coming together and determining if it is a good idea or not. The idea of conciliar decisions would prevent poor decisions being made by one man.
What's interesting is, the Greek Orthodox Archdiocese, along with the Antiochians, Orthodox Church in America (OCA) and many other jurisdictions all follow the Gregorian calendar most of the year. But when it comes to Pascha, they follow the Julian calendar. Why is that? The reason for the calendar switch is that these Orthodox churches continue to believe in the decision of the First Council of Nicaea, that the churches all celebrate together. It's most important for the Orthodox churches to celebrate together. For the churches that have not jumped onto the Gregorian calendar, the rest of the Church joins them in celebrating Pascha on the Julian calendar.
Liturgically speaking, most "Orthodox Countries" still use the Julian Calendar liturgically. While here in the United States, Western Easter is often celebrated with pastels and egg hunts, in some cities in eastern Europe, cities are shut down, celebrations are had in the streets. Our experience here in the United States is very subtle but if we ask those who REALLY celebrate in other parts of the world to conform to fit our experience, you'd find it's a little more difficult.
One thing that is important to point out: Contrary to popular belief, modern Jewish Passover plays NO ROLE in determining when Orthodox Pascha is celebrated. While Pascha (meaning Passover) is the fulfillment of Passover and took place during the period of Passover, the modern Jewish calculation and calendar play no part in determining when we celebrate Pascha (Easter). The fact is, Orthodox Easter has happened before Jewish Passover was over numerous times.
While it's not the biggest issue in the life of the Church, it would be nice to celebrate with all those who believe in the resurrection of Christ. Hopefully this sheds some light on the issue so that when you're asked, you might have an answer. Perhaps one day that will be one more thing that unifies us all, rather than divides.
If you need to give a real short answer: The Orthodox Church uses a more ancient calendar.