Question: I have been hearing this frequently that gaussian processes is a smoothing operation. I didn't get what they mean by that. Any clarifications guys?

Answer: 
One way to think of gaussian processes is a kernel density estimation with a fixed-finite number of kernels not fixed at the data. In this interpretation, the arguments for why KDEs are smoothing apply.
From the book Gaussian Processes for Machine Learning by Rasmussen and Williams; If you're doing GP regression, and you want to predict a value at a point $\mathbf{x}^\*$, the posterior predictive mean is given by:

\begin{align\*}
\overline{f}\_{\*} = \mathbf{k}^T\_\* (K + \sigma^2\_n I)^{-1} \mathbf{y}
\end{align\*}

where $\mathbf{y}$ is the vector of observed outputs. Note this is a linear combination of the observed values $\mathbf{y}$, that is it can be rewritten as:

\begin{align\*}
\overline{f}\_{\*} = \sum\_{c =1}^{n} \beta\_{c} y^{(c)}
\end{align\*}

As I understand it using a linear combination of the observed values a your predicted mean is a sort of smoothing.