Suppose you already know that a problem $Q$ is NP-hard. Now you need to show that problem $P$ is NP-hard.
Note that it's very informal and intuitive idea.
We'll show $P$ is as hard as $Q$, which proves that $P$ is also Np-hard. We know that $Q$ is very hard problem. Now the idea is like proof by contradiction. Assume $P$ is not that hard like $Q$ and I could have an easy algorithm. Now, I need to get some contradiction. So what can I do? I can reduce $Q$ to $P$, i.e, we have an easy black box algorithm for $P$ and we can use that to change an input of $Q$ to input of $P$ and use that black box to get a solution for $Q$. Oh! I have easily solved $Q$. But, this contradicts the fact that $Q$ was hard. Thus our assumption was wrong and $P$ must be also as hard as $Q$.
The following image will not let you forgot the direction ever.
$Q$ known to be NP-hard, $P$ claimed to have a polytime algorithm.