The fine-tuning argument is actually part of the teleological argument.
The way the universe is arranged, from the micro to the macro, is just so. It turns out that everything is just right for intelligent life on Earth. This is so amazingly improbable it must have been done on purpose.
Actually no. Look at the size of the universe (in particular, look at the Hubble Ultra Deep Field image). Compared to the size of the universe, life on Earth is an invisible dot on an invisible dot on an invisible dot on an invisible dot. What kind of intelligent creator would make something so mind-bogglingly vast, just so that an infinitesimal part of it could develop intelligent life, while the rest of creation remains – to an almost universal degree – dispassionately deadly? Only an incompetently wasteful one.
The reason why the universe appears fine-tuned to us is that we are a product of it. If the universe were "tuned" differently, we would be different (probably utterly and incomprehensibly different).
Some people invoke the idea of the multiverse – a possibly infinite number of universes, all slightly different, existing in parallel, and unable to communicate with each other in any way. This hypothesis may be useful as a thought-experiment, but it's unfalsifiable, so of little practical utility. The idea is that there are so many of these parallel universes that all combinations of the values of physical constants will exist, somewhere, however improbable. We just happen to be living in one that contains at least one planet suitable for the evolution of intelligent life.
Here's Douglas Adams on what has become known as the Anthropic Principle:
"...imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!' This is such a powerful idea that as the sun rises in the sky and the air heats up and as, gradually, the puddle gets smaller and smaller, it's still frantically hanging on to the notion that everything's going to be alright, because this world was meant to have him in it, was built to have him in it; so the moment he disappears catches him rather by surprise."