Learn Dutch: Het leer, dat erg stug is, wordt steeds zachter. - The leather, which is very stiff, is getting softer and softer.

This is a non-restrictive relative clause. It adds extra, non-essential information about het leer. If you take it out, the main sentence (Het leer wordt steeds zachter) still refers to the same specific piece of leather. Just like in English, we use commas to separate this extra information from the main clause.

Would the meaning change if we removed the commas from this sentence?

Yes. Without the commas, it becomes a restrictive relative clause, which limits or defines the noun. Het leer dat erg stug is would imply there is other leather around that is not stiff, and we are specifically talking about the stiff one. By using commas, we show there is only one batch of leather being discussed, and its stiffness is just an added detail.

Why do we use dat instead of die for the relative pronoun here?

The relative pronoun always has to match the gender of the noun it refers back to. Because leather is a neuter noun in Dutch (het leer), the matching relative pronoun is dat. If we were talking about a non-neuter word, like de riem (the belt), we would use die.

Why does steeds zachter mean softer and softer rather than always softer?