I want to colour an unclosed shape, to be more precisely what I mean:
Here is where the person creates 2 lines and suddenly he makes the background (fill) green between the 2 lines:
I want to do that as well, but I have no idea how...
All you need to do is treat your open path the same as you would a closed one.
Click on it, change its fill. That simple.
It works for all sorts of differently shaped paths:
After examining the video you posted more closely, I can see you are going about this the wrong way.
The guy in the video is not filling an open path.
He is creating green rectangles to fill the space between his outlines. Look at the image below and you can see the outlines of the paths he used to make the leg/foot: