Can somebody briefly explain me the tension of the string, and has it any relation to any of the newton s laws?

Explanation:

I'll give it a go.

In simpler cases, tensions in strings are typically caused by some weight attached to the end of them. You could use Newton's 3rd Law to describe this phenomenon.

So because the weight is pulling on the rope with a force, an equal and opposite force is enacted throughout the rope. That equal and opposite force is what we call "tension".

*Note that if the weight of the rope is negligible, or you are ignoring it for a specific problem, then the tension is the same throughout the rope. In more complicated cases, the rope does have weight. In these cases the tension changes at different lengths of rope.