Blanca is a mysterious cat whose face you can draw on.
How do I get Blanca in my town?
Prior to the closure of the Nintendo Wi-Fi Connection, to get Blanca to show up in your town, you could use the phone in the attic of your house and say that you are OK with visits from the mysterious cat. Then you could connect to Nintendo WFC and open your gate. You didn't need to have visitors come from other towns. After you closed your gate, you could look around your town for a chance to find Blanca wandering around somewhere outside.
How do I draw a face?
As stated above, it is no longer possible to get Blanca in your town. Back when you could draw Blanca's face, it was just like drawing a pattern in the Able Sisters' store. You could choose a color set at the bottom, choose a tool from the toolbar on the right, and draw in the center. If you chose a different color set, the colors in your current drawing would change to match the color set. It was not possible to mix colors from different sets.
Who is Blanca the cat?
Nobody really knows. Blanca is a mysterious cat (THE mysterious cat, according to the phone in your attic) who used to show up in your town back when the Nintendo WFC was still available.
What's wrong with Blanca's face?
Blanca seemed to want to hide their identity, so if you talked to them, they invited you to draw a new face.