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: 
*Multiplication* in your first sentence is *term-by-term* multiplication: $z[n] = x[n]y[n]$ for all $n$. Convolution, for discrete-time sequences, is equivalent
to *polynomial* multiplication which is *not* the same as the term-by-term
multiplication. Convolution also requires a lot more calculation: typically $N^2$
multiplications for sequences of length $N$ instead of the $N$ multiplications
of the term-by-term multiplication.

The key point of Fourier analysis is that term-by-term multiplication in *one*
domain is the same as convolution in the *other* domain. So, in order
to calculate the results of a convolution, you can either do it directly,
using $N^2$ multiplications, *or* transform to the other domain, do a term-by-term
multiplication, and transform back. This requires two transformations
to go from one domain to the other, $N$ multiplications in the other domain,
and one *inverse* transformation to come back to the domain
where the convolution result is needed. This more complicated process
can, in fact, require less computation because the transformations can
be done very efficiently via the *Fast Fourier Transform* (FFT) algorithm
which requires about $N \log N$ multiplications. So, compare the computational
effort in calculating the three transforms and doing the term-by-term
multiplication
to $N^2$ to see if the FFT gives you a more efficient method of computing
a convolution.
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 .