The following is an excerpt from one of the essays I wrote for the Biola Certificate in Christian Apologetics program, which I highly recommend. (I'm almost done now, just have to finish up part 3!)

The Moral Argument is an argument for the existence of God. This argument could be proposed like this:

#1 Objective moral laws exist.
#2 A moral lawgiver, God, is the best explanation for the existence of objective moral laws.
#3 Therefore God exists.

An important distinction that should be made at the outset is that the argument does not claim that a person who does not believe in God cannot be moral, but instead claims that non-theistic explanations of morality can describe what is moral but cannot explain why it is moral. If this argument is true, a non-theist may still live a better life than a theist, but would not be able to explain how a moral obligation could exist merely by observing how things are.

Regarding premise #1, there can be only two possible options with regard to moral values: they are either objective or subjective. A synonym for subjective morality is moral relativism, and there are many serious problems with this view of morality. Besides the fact that  practically speaking, when pressed, few people honestly hold to true subjective morality , if there is no objective right and wrong, many concepts such as fairness, guilt, tolerance, altruism, and shame become meaningless.  There are many other serious logical and practical problems with relativism.  Therefore, almost no one accepts the idea that morality is relative.

Where then did moral absolutes (laws) come from? Premise #2 above posits that the best explanation for this source is God. Since these moral laws remain valid and true whether anyone believes in them or not, they could not come from evolution, social consensus, or personal preference. These laws are standards that exist independently of our own human existence and must have a source in something that exists outside of our material universe (since they are immaterial). This "something" is God, a personal being who provides both the nature upon which the laws are based and the volition through which they have been instituted.

Further reading:
Why can't morality have just evolved? – Read Monkey Morality by Greg Koukl.
A longer discussion of the argument – Read The Moral Argument for God's Existence by Paul Copan.