Although the Christian Church truly began with the birth of Christ, the Mennonite way of the faith goes back to the 16th century with the Protestant Reformation. The Protestant Reformation essentially was the movement where Roman Catholics began to disagree with and then attempt to reform major aspects integral to the faith. Unsuccessful in their reformation, people ended up separating from the Roman Catholic Church. There ended up being many church branches stemming from the Reformation, Mennonites included.
The first Mennonites came mainly from Swiss and German roots, with many of the important martyrs of the early church coming from the area around Zurich. Mennonites took their name from Menno Simons, a Dutch Roman Catholic priest. Upon studying the Scriptures Menno Simons determined that infant baptism was not in the Bible. He came to believe that baptism should be a conscious adult decision. Those with this belief are called Anabaptists. It was the distinguishing feature to Menno Simons' movement because every infant born in Western Europe was baptized into the Roman Catholic Church. He converted to the Anabaptist faith and helped lead it to prominence in Holland by the mid-16th century. Due to the dominance of the Roman Catholic Church and the nature of his reason for leaving the Roman Catholic Church, he and his 'followers' were the victims of much persecution.
To escape this persecution, many Mennonites fled western Europe for the more accommodating religious climate of the Americas or Catherine the Great's Russia (1770ish), giving these two groups distinctly different cultural heritages. The Russian Mennonites were eventually forced out of Russia in the last half of the 19th Century and the early 20th Century, and many migrated to the western states and provinces, where today there is a large Mennonite population. (My grandparents were in this category)
Swiss German Mennonites migrated to North America in the 18th and 19th centuries, settling first in Pennsylvania, then eventually across the Midwestern states. Today large Mennonite populations can be found in Pennsylvania, Ohio, Indiana, and Kansas, although Mennonites live in all parts of the United States and the world. Many people in the older generation of this group continue to speak a low German dialect called "Plautdietsch" and eat traditional foods.
The Amish, who separated from the Mennonites in the late 1600's, are widely known for their plain dress and rejection of modern technology and conveniences.Unlike the Mennonites, they form an exclusive and tight-knit community, with the church dictating much of what may or may not be done: for example, each local church district would dictate rules regarding the use of telephones, if indeed they are permitted at all.
While certain conservative branches of the Mennonite church still dress simply and require women to wear head coverings, Mennonites generally are not culturally separatist, choosing to embrace the larger communities outside of their church rather than forming a separate community around the church. Where the Amish believe in keeping themselves spiritually focused by limiting their interaction with modern society, Mennonites believe in practicing Jesus' teaching of service to others in a broader context.
* My intent is not to judge or criticize the Roman Catholic faith but to explain the history behind Mennonite Christian faith. I have great respect for Catholics and their faith even if it is not my personal belief.
Sources:
http://history.mennonite.net
Wikipidia - key words Protestant Reformation and Menno Simons