By billions and billions here we actually mean 10-20 billion (most people believe a figure of 12-16).

"The Big Bang"* describes a very hot period of time in the universe. The universe expands and cools in a very nice thermodynamic way. I place the quote marks around the big bang because it is an incomplete theory. From observations (expansion of the universe, the cosmic microwave background) we infer a time of much greater density and higher temperature.

We still don't know why the universe was like this, nor how it came to be like this. The term Big Bang is more a statement of initial conditions than a theory that explains where all the stuff came from. Not to be on a downer, a lot of good work is being done at the moment and within the next few years the theories which try to explain the initial conditions will be tested. These are theories of inflation and flavors of string-theory.

When the universe gets as hot and dense as it was during the big bang the laws of physics we have now don't work. The problem is that we can't describe gravity on very small scales. usually that's ok because on very small scale (think the size of an atom) you usually find small amounts of matter (an atom for example) and gravity is so weak that we don't have to worry about it. Things during the Big Bang were much more dense than they are now. Imagine squeezing the earth into a space the size of an atom, imagine squeezing an entire galaxy into this space, you can bet that gravity is going to become very important. It happens when you get a mass called a Planck Mass into a volume of space which is a (Planck length)3

Before things get that crazy the physics we have now works very well, thank you very much. So much so that we have decided to call it "the standard model" At early times there was so much energy floating about that matter and anti-matter popped into existence, then annihilated each other. This went on for a while but due to a deep asymmetry in nature slightly more matter was created than anti-matter. This eventually condensed out as the universe expanded and cooled. In about 11 minutes after the point at which our physics doesn't work. The technical term for stuff in the universe before the matter froze out is Yelm.

The matter that we were left with was hydrogen with a little deuterium. No carbon in sight. Over (10 billion years of darkness after the freezing out untill the first stars are formed, astronomers refer to this as the "dark ages") time under gravity this hydrogen bunched together in stars.

Stars are pretty neat. No one known in detail how they work. In general they are giant ovens that do exactly what the The Custodian mentioned. They do some other cool stuff to. All of the carbon we have around us was baked in stars. Planets formed from the detritus that is left around a newly forming star. After many generations of star formation, death and rebirth you get a healthy mix of elements floating around the place. Anything heavier than Iron has to be made in a supernova explosion, so while the carbon that makes up most of us can be baked in a regular star gold, silver, plutonium this all has to come from a supernova. This has prompted the idea We are all particles of stardust held together by angels.

A star form from a huge cloud of gas, it is a very complicated process, but many interesting molecules can be formed in the process (a giant cloud of alcohol, larger than the solar system was found last year by astronomer, unfortunately it was too far away be takes advantage of) In recent months some astronomers calculated that in the formation of a star you can form two of the base-pairs for DNA can be made this way. They are working to see if the other base-pairs can be created in a similar fashion.

This does not answer where biological life came from, but it is interesting.

* the term was coined by Fred Hoyle as a derogatory remark, but it stuck.