“Evangelical” is a broad term that means “having to do with the gospel.” Medieval reform movements such as the Dominicans and Franciscans, for instance, used the term “evangelical” to describe a way of life patterned after Jesus and the apostles (specifically a life of poverty dedicated to preaching the Gospel and serving others). The Protestant Reformers used the term to describe their movement (“Protestant” was a label applied by Catholics), because they believed that they had recovered the Gospel (i.e., the message of justification by faith). In the late 17th and 18th centuries, many Protestants believed that the Protestant churches had become spiritually dead, focused on correct doctrine and/or respectable morality rather than on a living faith in Christ. In Germany, the movement to emphasize experience and personal commitment was called “Pietism”–in the English-speaking world, it was generally called “the Evangelical Revival.” Methodism originated as part of this movement, but it was only part.
In America evangelicalism became the dominant form of Christianity. The “First Great Awakening” in the colonial period and the “Second Great Awakening” in the early 19th century brought many people to a personal commitment to Christ and transformed American Protestantism. Many more people became active Christians (one of the myths of colonial America is that it was a very religious society–outside New England this was by and large not the case, especially on the frontier–the Great Awakenings, especially the Second, changed this), and the denominations that favored an emotional religion focused on personal experience tended to be the growing ones. (This meant particularly Methodists and Baptists, though Presbyterians participated as well–indeed pretty much all Protestant denominations were affected to some extent.) By the mid-19th-century, most American Protestants saw themselves as part of an “evangelical” alliance that emphasized the authority of Scripture and the necessity of personal conversion. This evangelical Protestantism was very ecumenical among Protestant denominations but extremely hostile to Catholicism. The same situation prevailed to a great extent in Europe, especially Britain, but less clearly than in the U.S.
19th-century evangelicalism started to break down in the latter half of the century, largely because of the growth of liberal theology among the educated clergy. Biblical criticism and to some extent scientific discoveries and theories such as Darwinian evolution (though I think the importance of this has been exaggerated) caused many Protestant intellectuals (particularly in Germany) to question traditional beliefs. (Actually there had been Protestant theologians who did this for a long time, but these currents became more dominant after about 1860.) The most basic way of describing this theology is that it separated out questions of history and science from questions of faith. You could be a devout Christian based on personal experience and the pursuit of personal and social holiness without necessarily believing that the Red Sea really parted or, in extreme cases, that Jesus really rose from the dead in a physical sense. So liberal Protestants used evangelical language (Adolf von Harnack’s
What is Christianity? is a really good example of this) without necessarily believing in things like the bodily resurrection which traditional evangelicals would have taken for granted.
Thus, in the early 20th century American evangelical Protestantism (and to some extent European Protestantism as well) broke up into two wings: the “modernists,” who accepted the liberal premise that you could be a devout Christian without necessarily believing in the traditional claims of Christianity, and the “
fundamentalists,” who insisted on certain doctrines and historical claims as being central to the Christian faith (the five “fundamentals” were usually listed as the inerrancy of Scripture, the virginal conception and deity of Christ, substitutionary atonement, the bodily resurrection of Jesus, and either the miracles generally or the Second Coming, depending on which version of the list you follow; the main difference is whether you insist on a “premillenial” version of the Second Coming, which some fundamentalists did/do). By the 1920s the fundamentalists were leaving or being kicked out of many of the major Protestant denominations, leaving people with more or less “modernist” views in control. (It wasn’t quite that simple. Many people remained quite traditional in their views in the big denominations.)
Ahhh, I haven’t gone to a good hymn sing in ages…probably since I left the Methodist Church for the Episcopal Church, although the music and hymnology in the Episcopal Church tends to be quite good as well. (After all, Charles Wesley remained a member of the Church of England to his death! 
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