Intelligent Design is the study of patterns in nature that are best explained as the result of intelligence.
-- William A. Dembski
The most famous version of the design argument can be found in the work of theologian William Paley, who in 1802 proposed his "watchmaker" thesis. His reasoning went like this:
In crossing a heath, suppose I pitched my foot against a stone, and were asked how the stone came to be there; I might possibly answer, that, for anything I knew to the contrary, it had lain there for ever. ... But suppose I had found a watch upon the ground, and it should be inquired how the watch happened to be in that place; I should hardly think the answer which I had before given [would be sufficient].
To the contrary, the fine coordination of all its parts would force us to conclude that
the watch must have had a maker: that there must have existed, at some time, and at some place or other, an artificer or artificers, who formed it for the purpose which we find it actually to answer; who comprehended its construction, and designed its use. 
Paley argued that we can draw the same conclusion about many natural objects, such as the eye. Just as a watchs parts are all perfectly adapted for the purpose of telling time, the parts of an eye are all perfectly adapted for the purpose of seeing. In each case, Paley argued, we discern the marks of an intelligent designer.
Although Paleys basic notion was sound, and influenced thinkers for decades, Paley never provided a rigorous standard for detecting design in nature. Detecting design depended on such vague standards as being able to discern an objects "purpose." Moreover, Paley and other "natural theologians" tried to reason from the facts of nature to the existence of a wise and benevolent God.
All of these things made design an easy target for Charles Darwin when he proposed his theory of evolution. Whereas Paley saw a finely-balanced world attesting to a kind and just God, Darwin pointed to natures imperfections and brutishness. Although Darwin had once been an admirer of Paley, Darwins own observations and experiencesespecially the cruel, lingering death of his 9-year-old daughter Annie in 1850destroyed whatever belief he had in a just and moral universe.
Following the triumph of Darwins theory, design theory was all but banished from biology. Since the 1980s, however, advances in biology have convinced a new generation of scholars that Darwins theory was inadequate to account for the sheer complexity of living things. These scholarschemists, biologists, mathematicians and philosophers of sciencebegan to reconsider design theory. They formulated a new view of design that avoids the pitfalls of previous versions.
Called intelligent design (ID), to distinguish it from earlier versions of design theory (as well as from the naturalistic use of the term design), this new approach is more modest than its predecessors. Rather than trying to infer Gods existence or character from the natural world, it simply claims "that intelligent causes are necessary to explain the complex, information-rich structures of biology and that these causes are empirically detectable." 
ARN Recommends: For more information about the basic concept of intelligent design, see the following resources:
Intelligent Design: The Bridge Between Science and Theology William A. Dembski
Mere Creation: Science, Faith, & Intelligent Design edited by William A. Dembski
Rhetoric & Public Affairs Special Issue on Intelligent Design John Angus Cambell, ed.
For those who are interested in the problem of pain and the role it played in Darwin's life and work, see:
Darwin's God: Evolution and the Problem of Evil Cornelius G. Hunter