I've actually been to their most important historic center, a place called Herrnhut, Germany in the far east, very close to the Czech border.
The Moravian denomination descends from the pre-Protestant Christians from Moravia and Bohemia--the 2 historic kingdoms which make up the modern Czech Republic.
About 100 years BEFORE Martin Luther, in the early 1400s in Prague, (about 200 miles or so from Luther's part of Germany) Bohemia, a monk named John Hus, saw a lot of corruption within the Roman Catholic church and strongly preached against it. Like all of Europe to the West, Bohemia and Moravia were firmly Catholic at the time--but had first been evangelized centuries earlier by eastern Orthodox...they really are on the border of eastern Europe.
Hus was protected by King Wenceslaus (yes, the one of Christmas Carol fame) and Hus had some of his thinking influenced by the English followers of John Wycliffe (as there was a royal connection by marriage at that time between Bohemia with England) whom the Roman Catholic Church had declared a heretic. Hus was called to a hearing by the Roman Catholic Church in Germany, and King Wenceslaus got a guarantee of "safe passage" for Hus so he journeyed over to the beautiful lake city of Constance.
Upon reaching Constance, Hus was immediately thrown into a dungeon, and was later tried and then burned at the stake. Guarantees to heretics were not seen as binding...claimed the Church.
Prague and Bohemia reacted an uproar, as John Hus was a popular hero--who had fought a lot of the corruptions of the rich and powerful...(in the richest and most powerful institution of the day, the RC Church). Long story short, a series of wars began, with 3 or 4 Czech groups, against orthodox Roman Catholic groups...and eventually the Roman Catholic forces won...and Czech Protestantism was forcibly crushed. Roman Catholicism was the official religion, and, as in all Europe at the time, other forms of Christianity were simply not allowed (under pain of, the stake...).
Fast forward to the 1700s. The Lutheran Protestant Reformation of the 1500s had not been permitted in Bohemia and Moravia--they were still officially Roman Catholic (while bordering the Lutheran states of Germany). However, some of the proto-Protestant Hussites still existed...secretly...throughout the countryside--even after 300 years of persecution.
A German count, who owned a large estate next to the Czech border, had become a very devout Lutheran--and had gone to seminary and became ordained a Lutheran minister. He was visited by a Hussite, who told him of the Czech bretherens' plight--just across the border. The Count, Rev. Ludwig von Zinzendorf, opened his estate up to these Czech religious refugees--and many streamed over, happy to live in peace according to their conscience.
Things did not go so well in Herrnhut (the new town on the estate)as the new immigrants, now that they were free... started to squabble and fight each other... so Count Zinzendorf put his foot down, and demanded that they meet together and pray...and agree to start living like New Testament Christians.
The Moravians (as they were now called) did start living out their faith...in a spectacular way--rarely seen since say AD 50. Many Germans now were attracted to come to this community of devout Christians. For the first time amidst Protestants and interest in foreign missions formed...and the hard working Moravians--supporting their own missionaries by home-grown industry in Herrnhut--sent out 2 of their number for every 1 that stayed home....
To this day, there are Churches in the South Pacific, or the Aleutian islands, or other way out of the way places, founded in the 1750s by the Moravians. They also re-instituted the New Testament practice of a "love feast" (think an elaborate pot-luck supper!), and had a 100 year 24/7 prayer chain (no I'm not kidding) ...(throughout their period of fantastic missions....). Many came as missionaries to America--and a few were missionaries to American Indians (while certain other Americans were killing them off...). Christmas also had particular significance to Moravians...hence the founding of Bethlehem, Pennsylvania.
I'm not certain the Moravians were ever completely officially pacifistic...however as someone indicated above, at some point they became so. However, they have no connection historically to the Mennonites or the Quakers, and they are not "Anabaptists" the name for early radical Protestants--as their theology has more in common with Lutheranism (and hence classic Protestantism). Probably the reason they would not participate in certain wars, is that they have always formed such independent, self sufficient communities...they never had a dog in the fight--hence just didn't fight. I believe today the Moravians are no longer officially or unofficially Pacifistic.
They are, as a denomination, much like most other mainline denominations...with all the same conflicts and problems with liberal theology....and I'm not sure I'd recommend Moravians as really special today.
However the early history of the Moravians is one of the most bright and shinning stars of all of Christian history.
A classic "Moravian Star"...a geometric form developed by a Moravian math teacher in the 1800s--and now one of the most popular symbols of Christmas all over the world. 