Question: I read that multiplication is convolution in frequency domain. I also understand that convolution is just polynomial multiplication. Can somebody explain what are the advantages of doing convolution in frequency domain? Also, i would like to know how to multiply two signals in time domain and what is the significance of it.

Answer: 
It is significant that you can do *time domain convolution* via *frequency domain multiplication*. This can be done in less time due to existence of *highly* optimized [Fast Fourier Transformation](http://en.wikipedia.org/wiki/Fast_Fourier_transform) algorithms.

Time domain convolution has great significance in DSP at least because this way we can apply a [FIR-filter](http://en.wikipedia.org/wiki/Finite_impulse_response) to a signal.
The convolution operation can be imagined as swiping a credit card ,each instance of both the signals are multiplied with each other.
In which case a bar code scanner is more like multiplication ,only two instances of each signals are multiplied .