A linear element satisfies the property (ies) of: 

Linear network: A network is said to be linear of it satisfy both superposition and homogeneity. A non-linear network does not satisfy both these conditions.

Superposition (Additivity):

if x1(t) → y1(t) and

 x2(t) → y2(t)

Then x1(t) + x2(t) → y1(t) + Y­2(t)

Homegenity (Scaling):

If x1(t) → y1(t)
Then a(x1(t)) → a[y1(t)]

Important Points:

Linear Elements: A linear element is one whose parameters do not change with voltage or current. It has primarily two properties: homogeneity and additivity.

Example: Resistor, Inductor, Capacitor

Nonlinear Elements: A nonlinear element is that whose parameters change with voltage or current. It does not obey homogeneity and additive properties.

Example: Diode, Transistor

A circuit is linear if and only if its input and output can be related by a straight line passing through the origin otherwise, it is a nonlinear system.