What is Biblical fundamentalism?

Biblical fundamentalism refers to the strict adherence of the 5 major fundamentals of Bible teaching:
1. Inerrency of the Bible,
2. Virgin Birth of Christ,
3. The Diety of Christ,
4. The Bodily resurrection of Jesus Christ,
5. The substitutionary Blood atonement of Christ on the cross.

This was strong among Presbyterian and Baptist Churches. Since the 20s, a number of Baptist churches continued with the emphasis and often refer to themselves as Fundamental Baptist (or Independent Fundamental Baptist).

Answer from a Catholic

Extracted from Catholicism and Fundamentalism - The Attack on "Romanism" by "Bible Christians" by Karl Keating, Ignatius Press, 1988
The basic elements of [Biblical] fundamentalism were formulated at the beginning of the 20^th century at the Princeton Theological Seminary at Princeton, New Jersey by Benjamin B. Warfield, Charles Hodge, and their associates. What they produced became known as Princeton theology . . .
Between 1909 and 1915 the brother Milton and Lyman Steward, - - - underwrote the Fundamentals, a series of twelve paperback books . . . that would set forth the fundamentals of the Christian faith and which were sent free to ministers of the gospel, missionaries, Sunday school superintendents, and others engaged in aggressive Christian work throughout the English-speaking world. Three million copies were distributed. Aside from studies of strictly doctrinal matters, there were attacks on modern biblical criticism, critiques of scientific theories, personal testimonies, commentaries on missionary work and evangelization, and accounts of heresies. The last category included essays on "Catholicism: Is It Christian?" and "Rome, the Antagonist of the Nation".
There were as many as fourteen points, most commentators agree on at least these five (1) the inspiration and infallibility of Scripture; (2) the deity of Christ, including his Virgin Birth; (3) the substitutionary atonement of his death; (4) his literal resurrection from the dead; and (5) his literal return in the Second coming.
The coiner of the word "Fundamentalism" goes to Curtis Lee Law, who, in an editorial for the New York Watchman-Examiner of July 1, 1920, defined "fundamentalists" as those "who mean to do battle for the fundamentals.