First, I should address the notion of what a singularity is. According to widely accepted theory, singularities are zones which defy the current understanding that we have of physics. They are believed to be at the core of most black holes. A black hole is an area of intense gravitational pressure. That pressure is theorized to be so intense that finite matter is actually compressed until it has infinite density. This area of infinite density is called a singularity. Our universe is thought to have begun as one of these infinitesimally small, infinitely hot, infinitely dense singularities. The where and why of it all we still don’t have a firm grasp of, but the big bang is the point at which that singularity suddenly began to expand and created our universe as it moved outwards.
Some scientists believed that if our universe was created by a singularity, there would have to be a background heat still in existence in the universe. To understand why a scientist would think there is still heat from the big bang you have to know that the universe is still expanding. Galaxies appear to be moving away from us at speeds proportional to their distance. This is called Hubble’s Law, named after the man who discovered this fact, Edwin Hubble, in 1929. This observation supports the expansion of the universe and suggests that the universe was once compacted. So, if the universe was initially compact and very hot, you would be abler to find some of that heat still. In 1965 two radioastronomers, Arno Penzias and Robert Wilson, discovered a 2.725 degree Kelvin (-454.765 degree Fahrenheit, -270.425 degree Celsius) Cosmic Microwave Background radiation (CMB) which pervades the observable universe. This is thought to be the remnant which scientists were looking for.
Another question that comes to mind is whether or not space and time existed prior to the big bang. A trio of highly respected astrophysicists have published papers plainly saying no. Steven Hawking, George Ellis, and Roger Penrose based their work on the basics of Einstein’s theory of general relativity. Their calculations led them to believe that time and space had a definite beginning and the beginning corresponds directly with the big bang. In other words, the big bang was the beginning of everything.
The big bang theory is not the only model that tries to explain the origins of our universe. There are several other theories, but the big bang is the most popular and well known. Here is a link the the NASA page about the big bang theory. Here on Universe Today we have a great article on the topic. Astronomy Cast offers a good episode about the large scale structure of the universe.