The idea behind a fine-tuned universe is basically this:
The fundamental forces - gravity, the strong and weak nuclear force, and electromagnetism - are all "tuned" to the perfect degree that they not only allow for life, but are "tailor-made" for it (a quote taken from John Gribbin and Martin Rees).
Stephen Hawking has even commented on this: "The laws of science, as we know them at present, contain many fundamental numbers, like the size of the electric charge of the electron and the ratio of the masses of the proton and the electron. ... The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life."