Einstein's General Theory of Relativity tells us that space is warped in the presence of mass or energy. A bigger concentration of mass means more warped space. It becomes like a deformed rubber surface so that anything moving in space in the region of the mass is deflected towards it.
The Universe is full of mass and energy, so of course the universe is curved on a large scale. A beam of light sent from a point might either keeps going forever, if space is flat or negatively curved, or travels in a large quasi – circular curve if space is positively curved.