The Big Bang is what scientists call the enormous explosion that started time, space, and the universe. The explosion started out extremely dense and hot, before rapidly cooling down. To this day space remains a few kelvin above absolute zero because of the initial temperature of the Big Bang. Physicists use this model to explain when the fundamental forces appear that govern how everything in the universe interacts.
This event happened 13.8 billion years ago (see interactive visualization below, or the time scale of the universe). All energy and mass in the universe was created directly or indirectly as a result of this event. This should not be confused with the explosion of a star 5 billion years ago that created the solar system (please see NASA's birth of worlds).
For more information about the Big Bang please see Space.com's explanation. For information on what the universe looked like for the 'First three minutes' please see hyperphysics, or Weinberg's 'First three minutes'.