Google definition is best
A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field.
explanation by sir Leeh
A Gaussian surface is a mathematical construct. Its use comes in computing the total charge enclosed within a volume by performing an integral over the enclosing surface. If you find the value of a Gaussian integral to be zero, that only tells you that the net enclosed charge is zero. For example suppose you have an electric dipole at the origin. The net charge is zero and the Gaussian integral over an enclosing sphere will be zero. But the electric field inside the enclosed volume is definitely non-zero. It just varies from point to point.