The Universe can be defined as "everything that exists". The Universe, proper, is the single largest object with a name, and represents the culmination of full three-dimensional space interacting with time, forming a four-dimensional existence.
The most common belief among scientists today is that the Universe originated with the Big Bang, an expansion of everything that exists from an initial infinitesimally small point about 15 billion years ago. The effects of the Big Bang can be seen today by the fact that the farther galaxies are away from us, the faster they are moving away from us. It can also be seen in the microwave background radiation which is the much-attenuated radiation that originated soon after the Big Bang.
The size of the observable universe can be calculated as a sphere with a radius equal to the age of the Universe in light years. Thus the observable universe is a sphere with a radius of 15 billion light years, approximately 1026m. However due to initial inflation of the Universe soon after the Big Bang, the actual size of the Universe is much bigger than what is observable. The observable universe contains approximately 1010 galaxies or 1021 stars.
The Universe has no boundary but may be finite. This may be understood by a three-dimensional analogy: the Earth has no edge despite the fears of putative flat-earthers that they might fall off the edge if they travelled too far, but nonetheless the surface of the Earth has a finite area.
There is some speculation that multiple universes exist in a higher-level multiverse. For example matter that falls into a black hole in this universe could emerge as a big bang starting another universe, or the universe could ultimately collapse back into a "big crunch" which would rebound as a new big bang. However all such ideas are currently are not testable and so cannot be regarded as anything more than speculation.
One important question of cosmology is whether the Universe is open or closed. Depending on the average density of matter and energy it will either keep on expanding forever or it will be gravitionally slowed and will eventually collapse back on itself. Currently the evidence seems to point to an open universe.
Analysis of the term "Universe"
The universe can be defined as "everything that exists". This however causes problems in some statements, such as "God created the universe". Thus a better definition of universe might be the space-time continuum which exists, and all the matter and energy contained therein. This definition would allow for the existence of entities (such as God or gods) outside the universe.
Other Theories of Origin
The observed evidence, namely redshift and the microwave background, can also be explained by the theory stating that the present universe was formed from the collision of two universes. Consider, if you will, a plane surface. Any two objects on that plane cannot occupy the same space: they will collide. Now If we add a third dimension, height, the two objects will appear to collide, but one travels over the other, clueing the observer on that a third dimension must exist. If we take our current universe and insert it into an area with more dimensions, then we cannot escape the universe nor can anything else enter our universe unless two universes collide. The theory goes that when they collide, they collapse together and invert themselves, creating one universe where there was two. This point of inversion is what we now call the Big Bang. It also nicely explains the lack of anti-matter.