The rating of a house reflects the appreciation the owner of the house has for your design. The better you design, the higher your rating will be. A higher rating will result in a bigger gem reward as well.
Each piece of furniture has a rating attached to it. This rating is based on the rarity of the furniture. The more rare a piece of furniture is the higher the rating is.
Each house has a set of likes and dislikes. For example a house has a like for red items and a dislike for yellow items. By placing a red piece of furniture its rating will be higher because it is red. Placing a yellow piece of furniture will result in a negative rating. So be sure to look at the likes and dislikes for each house.
Synergy happens when a piece of furniture has more than one like. Its rating is than boosted even more! For example a house likes the color red and likes the category art. When you place a red piece of art synergy happens. The rating of that item will have three boosts.
When you place one item too many times it may result in a negative rating. So be sure to check the overall rating when placing duplicates of a single item.
Sometimes pieces of furniture fit both the like and dislikes of a house. This might cause your overall rating to go up or down. Be sure to check for synergy in that case. Sometimes the boost synergy gives to the rating of a piece of furniture is higher than the negative rating it gets from a dislike.
The rating of a house is converted into gems. This means that a higher rating will result in more gems per hour. The actual conversion rate of rating to gems may change with each update of the game.
Once you finish all the objectives in a house you are allowed to remove all pieces of furniture. Sometimes this is needed to get the best possible rating.