Well, I’m a Catholic who studied his Church history, so I know a little about this, but mind you, I’m no expert.
In the beginning, all Christians were of one faith—the “catholic” faith. The word literally means “universal”, and since there was only one Christian body, it was more or less true, if you exclude the “heretical” bodies such as Gnostics and Arians, which we won’t go into.
The Roman Empire, at the time of Emperor Constantine (who legalized Christianity and made it the state religion—this was in the 300’s AD) was split into two halves. The Western half had its capital in Rome, and the people spoke primarily Latin. The Eastern half had its capital in Constantinople and the people spoke primarily Greek. (The dividing line between these two sections of the Empire went right down through what is now Rumania.)
The Christian (or “catholic”, if you will) Church began, over a period of many hundred years, to drift apart, east from west. The two sides couldn’t quite agree on which day Easter should be celebrated on, for example, and as has been mentioned, there was that little article in the Creed about the Holy Spirit. In the West, where people spoke Latin, the Roman government had collapsed, and there was political chaos; the only institution which remained intact was the Church. As a result, the Pope (being the only guy left with any authority on anything) gained a lot of prestige, and later, political power, which in the long run was a detriment rather than a help. (Religion should always stay out of politics, IMHO.) The Pope, who was ostensibly the successor to St. Peter, 1st bishop of Rome, felt that he should be the leader of the entire Church, since St. Peter was the leader of the original 12 Apostles. The folks over in the Greek-speaking side, however (where, by the way, the Roman government was still in power and still perfectly stable; the Eastern Roman Empire actually lasted until 1453, although in history books it’s usually referred to as the “Byzantine Empire”) felt that all the bishops should be equal and work in concert together. As a result, friction built and built.
Finally, in 1056, the squabble reached a head, and the Pope excommunicated the Patriarch of Constantinople, who reciprocated in kind. The whole thing was more about power than faith, but people are like that, as we all know. From this point on, the Greek Church became known as the Orthodox Church, and the Latin Church became known as the Catholic Church, and they went their own ways. Eventually, the Orthodox churches developed along national lines, such as Greek Orthodox, Russian Orthodox, Ukrainian Orthodox, etc., but they all more or less considered the Patriarch of Constantinople as figurative head of the Church, although his decrees were not binding. The Catholic Church became known as the Roman Catholic Church, due to the headquarters being in Rome. Here, however, the Pope reigned supreme, and his word was binding on the entire Western Church. There were also a number of Eastern churches that did not follow the split in the East, but remained loyal to the Pope; these became the Syrian Catholics, the Melkite Catholics, etc., but they were (and are) really a unified part of the Roman Catholics----it’s all one Church, they just use variations in their liturgies.
So, up until the 16th century, you now had two Christian bodies—Roman Catholic and Eastern Orthodox. Over the 500 years between 1056 and 1517, the Catholic Church got rather corrupt in high places, and was badly in need of reform. However, the Popes and high ranking churchmen were dragging their heels, because, well, people are like that, as we all know. Finally Martin Luther rebelled and formed the Lutheran Church, and this sent waves throughout Western Europe—a lot of different Protestant bodies popped up, but eventually they settled down into two camps: Lutheran, based on Luther’s teachings, and Reformed, based on John Calvin’s teachings. So now you have three Christian bodies: Catholic, Orthodox, and Protestant. The Protestant bodies have, unfortunately, been unable to agree with each other on many different subjects, and they have continued to splinter to the point where there are hundreds of Protestant denominations in the world. To be fair, there have also been groups of Catholics who have split with Rome over the years, but by doing so they automatically become more or less Protestant, and not simply “another” Catholic church.
So, in today’s world, you have the Roman Catholic Church (usually just shortened to “Catholic”) with it’s small number of Eastern Catholic churches in tow; the various Eastern Orthodox churches, still organized along national lines; and the hundreds of Protestant churches----Lutheran, Baptist, Methodist, Anglican, Presbetyrian, Reformed, Fundamentalist, etc., etc. That’s the history, in a nutshell. As to the reasons why these developed, that would take a week to explain, and this post is already reaching the status of a Russian novel, so I won’t go into all that, other than to say that that’s how people are, as we all know. People are messy, and anything run by people, even churches, are bound to be messy as well. But, there’s always the happy little thought that God loves us all, even if we’re messy. Isn’t that nice? 
I hope this helps answer your question…