Laplace Transform is a complex function of complex variable.
It's often restricted to functions of time.
It is used to solve differential equations in control engineering, electrical engineering a lot.
It transforms ODE to Simple algebraic equation which can be solved easily..
s in Laplace transform is nothing but a complex number real and imaginary part.
s is called frequency domain in which
real part shows time constant of exponential growth and imaginary part shows frequency of simple harmonic motion.
In an AC circuit, there is a power source with sinusoidal current and other stuffs related to it..
Hope it helped you