Summary: Simply put, Conservatives favor maximizing individual liberty under minimal government while Liberals push for socioeconomic egalitarianism directed by government authority. The two worldviews tend to be mutually exclusive and rest on contrasting beliefs regarding man's basic nature.
There’s an old joke which says that “There are two kinds of people in the world: Those who believe that there are two kinds of people in the world and those who don’t.” In the realm of politics, that claim comes close to a truism. The most recent presidential elections and the war in Iraq have emphasized a growing and bitter fundamental discord between the so-called Liberal/Progressive Left and the Conservative/Traditionalist Right. This discord is currently in an acute stage of a chronic condition of clashing worldviews the roots of which are traceable at least to the time of the French Revolution (1789). It was, in fact, the seating arrangement in the French National Assembly (radicals/dissidents on the left; loyalists on the right) which resulted in the terminology we use today.
Thomas Sowell  has detailed this Left-Right political divide in terms of “…two long traditions of social thought”, or “Visions”, arising from two fundamentally different perceptions of human nature. One perception (the “constrained vision” in Sowell’s terminology) considers man’s nature as innately fixed and driven by incentives that further his personal well-being, status, esteem, and the fundamental concern for his self-reliant survival. Contemporary Conservatism is rooted in this perception of man’s essential nature which stresses the primacy of the individual and maximization of his liberty within a proscribed framework of laws to maintain civil order.
Since man, as seen in this constrained, or "tragic" vision, is at his core immutably driven by self-interest, so too will be those individuals who populate the ranks of government. Consequently, government itself must be viewed warily and its reach and authority kept to a minimum. Man is master, government his servant in this more traditional world view. Increasing intrusion of government into the social and economic affairs of man (now via self-perpetuating bureaucracies effectively insulated from the voting public) is to be kept to a minimum.
In contrast to this traditionalist worldview stands a more idealistic perception that the nature of man is completely flexible with an unlimited potential to "...act under the influence of a socially beneficial disposition, rather than simply in response to ulterior motives." This is the "unconstrained vision" in Sowell's terminology. Implicit in this view is the need for an activist, top-down government leadership to set, implement and manage national agendas aimed at achieving government-prescribed social and economic goals. This leadership is to drawn from a presumed intellectual elite wherein "... the special knowledge of the few [is] used to guide the actions of the many." It is this belief which informs the core of the political Left and contemporary Liberal/Progressive thought. This worldview requires a dominant central governing authority including numerous regulatory agencies to insure compliance with presumably socially beneficial edicts.
Such large, centralized authority, however configured, is anathema to the conservative mind which sees it as the doorway to totalitarianism. Potential tyranny notwithstanding, achieving an egalitarian socioeconomic equality-of-condition remains a primary focus of the Left. Thus emerges the irreconcilable conflict between the two worldviews:Freedom of the individual decreases as the size and scope of government increases. As Horowitz  has put it:
Ever since the French Revolution, radical 'equality' and conservative 'liberty' have opposed each other as the defining agendas of Left and Right."
Some other manifestations resulting from these conflicting worldviews have been noted by Pinker  who writes that today's Left and Right political factions each represent:
an astonishing collection of beliefs that at first seem to have nothing in common; viz.; ...if someone is in favor of a strong military, for example, it is a good bet that that person is also in favor of judicial restraint...will br tough on crime... in favor of lower taxes ...and [be a proponent] of laissez-faire economic policy.
Anyone supportive of this cluster of beliefs might well turn up in a button-down shirt at a Republican Party affair as an unwitting adherent of Sowell's "constrained vision" of human nature.
Pinker  adds that the
opposing positions cluster just as reliably: if someone is sympathetic to rehabilitating offenders, or to affirmative action...chances are he will also be a pacifist, an environmentalist, an activist, an egalitarian, a secularist and a professor or student.
A person embracing this set of beliefs would likely feel at home, sandal-clad, at a Democrat or Green Party function as a proponent of a collectivism and a believer in man's potential for perfectibility.
These worldviews are not necessarily mutually exclusive, but most of the politically-engaged (a relatively small sub-set of the overall population) generally support one to the exclusion of the other.
The question is why have these two conflicting visions with their corresponding political differences persisted essentially intact philosophically over the centuries? Do politically committed individuals arbitrarily choose their political biases or just succomb to persuasive others? The historical duration, unyielding contentiousness and specifics of the conflict suggests that political views may be innate; that is, acquired genetically. Again, Pinker  notes:
Liberal and Conservative attitudes are heritable not, of course, because attitudes synthesized directly from DNA but because they come naturally to people with different temperaments.
What then is it that determines ones "temperament"? A growing number of studies - recently aided by magnetic resonance imaging (MRI) and positron emission tomography (PET) brain scans - suggest the answer probably lies in the prefrontal cortex of the brain and therefore be innate and heritable. If so, our future political discourse will need to recognize this fact and adjust accordingly. Emerging evidence for the existence of an innate, rather than socially conditioned, political bias is the subject of another commentary elsewhere on this site.
Tags: Political Bias, Genetics
 Sowell, Thomas, "A Conflict of Visions", Basic Books (Perseus), N.Y., 2002, 29
 Sowell, 19
 Sowell, 42
 Horowitz, David, "The Politics of Bad Faith", The Free Press, N.Y., 1998, 148
 Pinker, 295