There are a variety of definitions, most of which can be put into the graphic below, grabbed from Wikipedia. Note that the scale is a log scale, so don't think the solar system is quite like is shown.
The most commonly accepted is based off of what is known as the Heliosphere. Simply put, the Heliosphere is where the force from the solar wind equals the force from the galactic pressure. It is about 100200 AU, perhaps a bit further, where 1 AU= the mean distance of the Earth from the sun.
Alternative definitions might include the distance of Neptune from the sun, 40 AU, the edge of the gravitational influence of the sun, which would be almost 1 light year (There are bodies orbiting at 1 light year away from the Sun), the distance of the Kuiper Belt, at around 200 AU, or a fair other number of methods.