It is the angle which the normal force N makes with the contact force when the equilibrium is limiting i.e when the condition of maximum Static friction
is reached

Consider a block of mass "m" resting on a horizontal surface .Weight W=mg of this block is balanced by the normal force (N) of reaction as shown below in
the figure.

Mathematically
W=mg=-N

if F is the contact force which each body exerts on the another body then this contact force can be resolved into two components

Perpendicular Components which is normal force N

Components parallel to the contact surface known as friction which is usually denoted by the f_{s},f_{k} or f_{ms}

Angle BCD represented by λ is angle of friction
Since N and f_{ms} are components of the contact force F,so we can write
Fcosλ=N
and Fsinλ=f_{ms}
or we can say
tanλ=f_{ms}/N
Also from the definition of static friction we know that
f_{ms}=μ_{s}N
So tan λ=μ_{s}
Thus we can conclude that coefficient of static friction is equal to the tangent of the angle of friction