Well, it's by Botero, so what did I expect.
The sculpture was bought by the City of Barcelona in 1987, and is called "The Cat of Raval" for its current location in the historical El Raval neighborhood. Here's someone's tourist movie of approaching the Big Cat:
Why such an exaggerated style? Every artist synthesizes the world they see in their own way. In Botero's case it started with a childhood in Colombia and the many Baroque churches in the area. Here's a website on Botero to help you learn more.
That's a fine cat, any way you look at it.