The universe is everything that exists.
I probably cannot improve on the first answer, but perhaps I can add a little clarity and perspective. Our world is one of eight orbiting the local star we call Sol or simply, the sun. The sun orbits a spiral galaxy we call The Milky Way, about once ever 220 million years. Our galaxy and the Andromeda galaxy are the two big spiral galaxies in a group of twenty or so mixed bag of galaxies we call the Local Group. Throughout the universe there are roughly 100 billion galaxies altogether.
The universe is the complete collection of this and all the space and matter in existence. It began with "the big bang" 13.7 billion years ago, and continues to expand at an increasing rate.
There may be other universes, universes in separate dimensions distinct from ours. The collection of all universes could be described as the multiverse or polyverse.