Gauss's law, basically stated, is that the flux through a surface which completely surrounds a charge Q, is equal to that charge Q over the Permittivity of free space. This is just a statement of the first of Maxwell's equations:

E·dA = Q ε0 S

Here Q is the charge surrounded by the surface S. This holds no matter what the shape or size of the surface S relative to the charge Q it envelops. This holds no matter how the charge Q is distributed within the surface. (One point charge, several charges totaling Q, etc.)

No matter how one shapes the shell which surrounds a charge or set of charges, the number of field lines that pass through the surface of the shell is always the same. This is of course the same with the force of gravity. The gravitational flux through any shell surrounding a given mass, is proportional to that mass. Thus, while specifically applying to the Electric field, Gauss's Law is really a principle with wider application than just in the field of electromagnetism.

Charge inside an irregularly shaped shell with field lines drawn.

Brief Explanation of Symbols;

Symbol	Brief Description
E	Electric field vector.
Q	Total electric charge encapsulated by surface 'S'.
ε0	Permittivity of Free Space (constant)
	Indicates a closed integral. (Integral over a closed loop or, when subscripted with 'S', a closed surface.)