The red star means it's a shiny.
That mark has been carried forward from Black/White/Black 2 and White 2. I can confirm, as for these games I:
- Pokétransferred a shiny from Diamond and
- Caught shiny Haxorus, Gibble, Dratini.
Another way to tell, the Pokédex number on the summary turns red, further confirming it's a shiny Pokémon.
Since I haven't seen any shiny so far in my Y game, and the picture the OP has uploaded doesn't show it, I can't tell if the Pokédex number shown on the summary also changes its color (if you're looking at a shiny Pokémon in this generation).