They're your standard cultivation rooms for cost-efficiency. It's half-complete because you don't have many resources when starting out, and you don't need a complete room yet. Once you do, there is a blueprint from one of the sects (you can acquire by visiting them - don't remember which one) which you put where the empty space is. Its Qi efficiency is far stronger then anything else until you reach mid-late game.

The one full room there is for body cultivators.

The full version of the rooms on the left side are for breakthroughs (you want them to accumulate Qi so you don't cultivate on them).

From what I remember the setup is designed for you to be able to build further as your get more of the resources you need. So every step from starting out to becoming strong.

I love the design. My current village looks so random and haphazard.

What are the half cultivation rooms on the right hand side?