I. The Physical Constants of the Universe
There are several properties of the universe that, if even slightly different from what they are now, would not allow life in any form to exist. For example, the matter/anti-matter balance, the amount of entropy, the gravitational constant, and so on. If these values and amounts were even off by a minimal amount, molecules would not even stick together and thus anything complex such as life would not be able to get started.
II. The Fine Tuning is Due to Chance, Necessity, or Design
There are three possible explanations for the fine tuning. Either it was an accident, the values could not have been different, or the values were deliberately set.
III. It is not Due to Chance
With so many logically available values, the chances are infinitesimal that they would all line up. Often it is said that if the universe were not fine tuned, we would not be here to see that it wasn't so. However, consider an execution squad of 100 marksmen. They train their rifles on the prisoner, aim, and fire. And all miss! Should the prisoner non-chalantly conclude "Well, of course they all missed! If they hand't, I wouldn't be here to see it!", or should he conclude that they missed on purpose?
IV. It is not Due to Necessity
There is nothing in physical law, or even proposals for the Theory of Everything, that predict our universe and it's tuned parameters over any others.
V. Therefore, the Fine Tuning is Due to Design
By eliminating the first two options, logically only the third option remains. The physical constants of the universe were deliberate set by an intelligence.
This article is a very brief intro. For a more in depth look, see the full article.