Stars indicate the quality of a part. Each part can have up to 5 stars. 
There are 5 tiers of stars depending on the material of the part: Wooden, Metal, Military, Golden and Carbon. Higher tiers mean higher quality. 
For example, a 1-star military part is better than a 5-star metal part.
The quality of a part is determined randomly, but the maximum possible result depends on the player's current Stage. You can check the Championship Map to see the maximum number of stars you can get in a given stage.
For example, if you are on Stage 15, you can obtain a golden part with only 1 star, but at Stage 20, you can easily receive a golden part with 5 stars.