In the context of Christianity (of course), what is a fundamentalist? And especially, how do they differ from mainstream evangelicals such as John Piper?
Evangelicals stem from fundamentalists, but have diverged since the 1950s. Theologically, they hold much in common, but primarily differ in their approach to dealing with society at large. It should be noted that neither is a "denomination" but rather a reforming trend that is cross-denominational, but bound by common purpose to reform the church, stripping it of historical (and liberalizing) accretions of practice, and returning it to the same position as "the first church," centering on its devotion to Jesus Christ.
Fundamentalists sprung up during the "back to the fundamentals" movement of the early 1900s. The seminal Work was a series of essays called The Fundamentals, highlighting such luminaries as R.A. Torrey, B.B. Warfield, and E.Y. Mullins. A brief look at the titles of the essays will highlight the issues important to these reformers.
This movement was deeply affected by the Scopes Monkey Trial of 1925, and largely disengaged from society shortly thereafter. While trying to reform the church, fundamentalists eventually came to the conclusion that they must be separate from the wider culture. Evangelists like Billy Sunday preached a Gospel of being removed from the society and rejecting all its ways. This included a rejection of politics as well as an eschewment of what the culture at large did.
By the 1950s, some in the fundamentalist movement like Carl Henry - the editor of Christian Century and founder of Christianity Today, came to believe that fundamentalists must engage the culture. In 1942, he founded the National Association of Evangelicals, and the point was to be "in the world, but not of it."
With Roe v. Wade, Evangelicals began to become more involved in politics, and helped bring about the rise of the "Religious Right." In the 1980s, fundamentalist Jerry Falwell introduced an innovation to fundamentalism when he sought to bring fundamentalists also back into the political arena, albeit in a more confrontational, "culture war" sort of way.
Theology Unplugged has two podcasts (7/9/06 and 7/8/06) that do a great job of tracing the history and divergence of the two - but basically boils down to approach rather than belief. John Michael Patton (Dallas Theological Seminary) says "Evangelicals are nice fundamentalists," by which he means, they engage rather than separate from the culture.
Wikipedea gives an apt enough definition, but speaking as a fundamentalist, I'll put it in my own words.
The defining characteristic of fundamentalists is that we hold fast to the fundamentals of the faith.
In short, we're old-fashioned, and often seen as the extreme right-wing Christians. We're the oddballs that the rest of society laughs at, specifically because we hold to such antiquated beliefs.
"Evangelicals" as a whole share many of these beliefs. Fundamentalists are essentially the ultra-conservative branch of Evangelicalism. The term "Evangelical" is simply more broad. Fundamentalism is a drill-down term, defining the more conservative subset within Evangelicals.
What is fundamentalism?
Fundamentalism first came to be called such with the printing of 90 essays describing various “fundamentals" of traditional Christian faith for distribution to Christian groups and organizations early in the 20th century. Considering the tenor of the times the political progressive movement (secularism) with associated interest in things like evolution, Marxism, and psychology, there was a defensive reaction to uphold that which was seen to be under attack.
One could make the case that early church creeds were a similar type of defensive reaction as well.
One can appreciate the desire to remain faithful to that which was received.
There are a couple of potential problems with fundamentalism. There can be a tendency towards legalism if the desire to hold to that which is true grows into a desire to control what others do. The second problem is that responding defensively can cause someone to focus on the fundamentals at the expense of other elements of faith and their walk with the Lord could become stunted.
The assault from the world was expected to be intense;
Fundamentalism in the US can be seen as an attempt to establish an anchor point to resit the swelling tide of the religion of secularism (the worship of man in general and self in particular) which replaced Christianity as the national religion.