Maybe I can help a fellow Christian out.
The Western Church and the Eastern Church separated in 1054 when the Pope of Rome and the Patriarch of Constantinople excommunicated each other. This event is often called the Great Schism. There are many reasons for this, but the big two are the authority of the Pope of Rome and the nature of the trinity surround the filioque clause of the Nicene Creed.
The Church at the time was battling a heresy known as Arianism. Arianism basically taught that Jesus, or God the Son, was of lesser divinity than God the Father. The western church solved the problem by adding "and of the Son" to a part of the Nicene Creed which discussed the origin of the Holy Spirit. This ensured that Jesus was considered fully God.
The eastern church had a big theological problem with this. They had confronted Arianism using different methods and felt that the addition of the filioque screwed up some other important theology involving the Trinity. Essentially they thought it muddled the differences in purpose between the Son and the Father.
However it was really the Pope that brought this to a head. He tried to impose the filioque using Papal authority which most of the western churches considered honorary. This combined with one Pope's death while messengers were in route set off the powder keg of tensions that had been brewing between both sides for centuries.