Hi!

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.

For example,

In an AC circuit, there is a power source with sinusoidal current and other stuffs related to it..

Hope it helped you