Methodism was a movement stressing piety, that grew out of 18th century Anglicanism (a.k.a. Church of England, "Episcopal" Church). The key proponent of Methodism was John Wesley.
The modern United Methodist Church is generally considered to stand in the "middle ground" of Christianity. We maintain much of the ritual of the Ancient Church, while being attuned to the lessons of the Reformation. Many "two denomination" families (e.g. a Baptist married to a Catholic, etc...) find common ground in the United Methodist Church.
The official denominational statement on the matter explains it well, "United Methodist doctrine is based on scripture, tradition, and reason."
More so than many other denominations, the United Methodist Church allows differences of opinion on doctrinal matters that are not essential to salvation. However, we are NOT an "anything goes" church.