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 13.7 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 (see Wikipedia:Light cone); many cosmologists assume that there are portions of the universe which we can not presently see. Also there may be a larger Multiverse. Still, even the observable universe is (theorized to be) bigger than the 13.7 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.
Religion and the Universe
Many religious people, particularly those believing in a theist religion, believe that their god created the universe, with some believing that the Earth is in the center of the Universe. Although many theists believe the Earth to be the center of the universe, for the most part, this is the uneducated minority. The common scientist and theist understand the sun to be the center of our solar system. Thus, the Earth cannot possibly be the center of the universe. In a sense, yes, Earth is in the center, but Earth is in the center only of the observable universe. Scientists cannot view other parts of the universe because the light waves from those parts have not come to Earth yet since the beginning of the Universe. The earth is not in any special or privileged place, if there are other conscious observers in other parts of the universe their observation point is the center of their subjective observable universe.
Since "universe" can mean both "the observable universe" and "the set of all things that exist," a common apologetics tactic is to treat the two concepts as if they were identical. This is a form of equivocation. When someone says "we know that the universe began to exist," as for instance in the Kalam cosmological argument, be sure to check which term they are using. The observable universe "began to exist" in the sense that it came into its current form during the Big Bang, but statements about the second term are not as clear cut.