The heliopause is the region is space where the influence of the solar wind and interstellar wind are in equilibrium - in other words where 'pressure' from matter originating from the Sun and matter originating from the rest of the galaxy cancel each other out. The region outside the heliopause is classified as 'interstellar space'.

It's known that the 'boundary' is farther than orbit of Neptune, but the size and 3-D shape is currently unknown. It has been suggested that it could be smaller on the side of the Solar System facing the Sun's orbital motion through the galaxy.

NASA's New Horizon space probe (launched 2006) is programmed to perform tests which might clarify.

Further details Wikipedia

Technical description from NASA (1994)