The amount of stars every character has is a rough indication of how good they are as computer-controlled opponents. It is mainly about their upgraded Stats, but not always about how strong their Power Shots are. But to be honest, stars don't really matter, so don't let them scare you. Some of the worst characters in the game have 5 stars. You can see these stars in the Arcade player select screen. All Characters have 5 stars, except the first 9 characters. It might be weird that there are so many Characters with 5 stars. This is because D&D Dream came up with the stars in the first Update and until then they were fairly good indicators. In the later updates, all characters had approximately equal stats, so they were all given 5 stars, even if their power shots were not worth it. This made the stars become redundant and rather useless, but they are still relevant to the characters from the first update.
In Survival, stars are used to help you recover your Balls. You can only recover 1-3 balls per match, and it depends on the time given. If timer gets to zero, no balls will be awarded.
(You can recover one more ball by watching a Video in the results screen after every match).