How big can a star get?
Short answer: We're not sure, but we know of stars up to about 2.4 billion km wide (e.g. UY Scuti). This is about 1,700 times the diameter of our Sun.
Long answer: First, it's important to understand the difference between size and mass. The size of a star measures how wide it is; the mass measures how much matter it's made of. You can have a star that has a lot of mass but it's squashed into a smaller size. In other words, a star can be larger but less massive than another star, or smaller but more massive.
Because stars are roughly spherical, we measure their size in radius or diameter. Other useful measurements are surface area and volume.
The size of a star is basically determined by two things: Its mass and the proportions of the elements that it's made of. Inside a star, elements such as hydrogen are fused together (nuclear fusion) and create energy that pushes outwards. At the same time, the mass of the star creates a gravitational force that pulls back inwards. These two forces find a balance that determines the diameter of the star.
Although we have a good general idea of how stars work, there are many variations for different types of star, and our knowledge is incomplete. We don't really have a good model to prove how big a star could get, so for now we'll just say they can get to at least 2.4 billion km wide.
Note: We have a better idea of much mass a star can have: Around 300 times the mass of our Sun, or 6 x 1032 kg.