Learn Hardcore Japanese: kono setai ha tiisai. - This administrative household is small.

Breakdown of kono setai wa chiisai.

What is the role of この here?

この means this and directly modifies a noun.

So in この世帯, この is attached to 世帯 and means this household.

Also compare it with これ:

You cannot say これ世帯. If a noun follows, use この.

What does 世帯 mean, and is it a common word?

世帯 means household: a group of people living together as one unit.

It is a real and common word, but it is a bit more formal or administrative than everyday words like:

You often see 世帯 in:

So the sentence sounds grammatically fine, but the noun 世帯 itself has a slightly formal, factual tone.

How is pronounced?