By fine-tuning is meant that there are numerous parameters, forces, and values that comprise our universe which, if they were even minutely different than what they are, the universe would either not exist at all or not be the sort of place where life could exist. In some cases the fine-tuning is calibrated to a precision which boggles the mind.
If, for example, the initial expansion rate of the universe at the time of its origin had varied by just one part in 10^120 the universe never would have formed. To give an idea of how enormous this number is, and thus how precisely set the expansion rate must have been, there are about 10^80 atoms in the entire universe.
No one questions that the universe is fine-tuned, but since a finely-tuned universe has profound implications for one's metaphysics, particularly the question of whether the universe is intentionally designed or not, and since the notion that it's designed is repugnant to naturalistic materialists, three alternative possibilities have been advanced to account for the universe's breath-takingly precise constants.
Lewis and Barnes have put together a short video to introduce their book and give a brief summary of each of these alternatives. Take a look:
For a list of some of the parameters and constants that are agreed by most scientists to be fine-tuned, and a lucid explanation of each, see the article by philosopher of science Jay Richards here.