Difficulties while understanding Convolution
The convolution sum is 
\begin{equation}
y[n] = \sum_k x[k]h[n-k]
\end{equation}
If you take the term corresponding to $k=0$, the contribution is $x[0]h[n]$. Similarly the contribution of $k=1$ is $x[1]h[n-1]$. Here, $h[n]$ is delayed by $n=1$. Similarly you can see how each term of the sum contributes to overall sum. The sum is taken over values $k$ where $x[k] \neq 0$ because only those terms contribute to the sum.