Humanism as a concept or philosophy dates back to the Renaissance. It was an attempt to reconcile the Bible (the religious foundation of the societies in question) with the newly-rediscovered writings of classical civilization. In an attempt to justify the investigation, appreciation, and study of ancient Greek and Roman thought (which, because the ancient writers were not Christian, presented religious difficulties to the more orthodox Renaissance mind), the Renaissance philosophers attempted to "distill" those ideas that both the Bible and the classics had in common. This was done to show that good Christians could study the ancients and appreciate their work without imperilling their soul.
The result of this work was a recognition that the both the Bible and the classics priviledged human freedom and virtue, as defined by Renaissance philosophers. The humanists argued that the classical attempts to encourage virtue were right in method, but wrong in direction (since the ancients didn't know Jesus). Likewise, they asserted that in order to do "good" (to be virtuous), a person must have the opportunity to choose (what they considered "freedom"). In a sense, their argument was that a person forced to tithe at gunpoint was not "virtuous," in that he was not making the choice to do good; rather he was just being forced to simulate the actions of the virtuous. This is what the early humanists meant by "freedom."
Our own founding ideals owe a great debt to the humanists, as their philosophy served as a starting point for the Enlightenment concepts of freedom and Natural Law. But recognize that the early humanists saw the principle goal of their work the reconciliation of the classics with Christianity, so as not to have to jettison the ancients in order to remain Christian (the Bible retained its privileged position.
Over time, the philosophy of humanism underwent sizable changes (many of them the result of Enlightenment philosophies). What is called "secular humanism" developed as an attempt to remove the Bible from its privileged position in humanistic philosophy. Instead of using the common concepts found in the Bible and other philosophies as a way of justifying the continued study of those philosophies, the more modern humanist moves the derived concepts of freedom and virtue to the privileged position, and asserts that all other ideas flow from them. In the secular humanist's conception, the Bible is another example of human virtue because it extolls (in part) human freedom and virtue, rather than, as was the case for the Renaissance humanists when the Bible was the assumed good that humanistic values were judged against. The modern secular humanist would reject those parts of the Bible that did not seem to meet the criteria of humanism (whereas the Renaissance humanist would have been horrified at the very idea).
Simply put, modern humanism is an attept to define the "good" based on universal principles that exist independant of any religious traditions. It's primary focus is on the "here-and-now" (i.e. human concerns), as opposed to spiritual or religious concerns. This was not the goal of the original philosophy, but it is what modern secular humanism has evolved into.