Residences are gained as you level your City Hall, just like other structures.
Residences increase your tax revenue by 6 silver per level. This amount is affected by your loyalty and Tax Office percentages
It's important to raise your Residence levels, but with limited build teams, you'll find residences being some of your lowest level buildings.
You get 10 residences in total. At level 100 with 10x level 100 Residences, you will be receiving 6,000 silver per tax collection from them.