The Big Bang Theory was first proposed by Georges Lemaitre in 1931. Later, others helped popularize the idea. He theorized that 14.5 billion years ago (this age has been increased and decreased over the years), a ball of condensed energy called a singularity exploded, and over the course of millions of years, the contents of that singularity spread out into the universe, forming stars, planets and solar systems. There are many problems with this theory. The following article explains the Big Bang Theory and its technical problems more in depth: http://www.answersingenesis.org/articles/ee2/big-bang
A growing group of scientists have written a letter to the scientific community pointing out the flaws: www.cosmologystatement.org. (Note: That link takes you to another site where the letter has moved. It is no longer located at the address you click on, but another website has adopted it.