The universe is generally understood to be everything which physically exists, including all forms of matter and energy, and all events that occur involving the two. It is sometimes contrasted with a supposed "other world" of some metaphysical nature (e.g., other "planes of existence").
According to the most widely accepted scientific theory, the universe consists of a four-dimensional continuum of spacetime (three dimensions of space and one of time) that grew out of an incredibly small "ball" of matter/energy (perhaps even a singularity, a dimensionless point) in an event called the Big Bang about 13.5 billion years ago.
It is currently unknown whether the universe extends beyond the observable universe, that part which we are able to observe (at least theoretically) from our particular vantage point at this particular time; many cosmologists assume that there are portions of the universe which we can not (presently) see. Still, even the observable universe is (theorized to be) bigger than the 13.5 billion light years that its age would seem to imply. This is because of the curvature of space-time; see Wikipedia's articles on the observable universe and the central ideas of general relativity for more information.