I'm sort of new to Altium, so any kind of detailed help would be very welcome... I need to create a PCB in altium that has copper all around with small plastic channels surrounding the tracks. Is it possible to create such thing (as described in the picture)? Do I have to create some sort of polygon around it?
Yes, you use a polygon copper pour (put the polygon on a copper layer) and connect the pour to the desired net if you want to use it for connectivity (it's generally bad form to leave copper floating without a good reason).
Copper pours can be a bit inconvenient to work with while you are manually routing a board so you can 'shelve' the polygons while you are working on other things. Today's computers are not fast enough to repour in real time, so you need to repour the polygon whenever changes are made that affect the polygon (such as moving a via).
As David said, your image looks like a milled PCB that would likely have been created by post-processing the Gerber output files to create tool paths.