In this passage, the word "prestigious" means that the School of Fine Arts in Barcelona is very respected and admired. It suggests that this school has a good reputation and is known for being one of the best places to study art.
To understand what "prestigious" means, we can look at a few clues in the paragraph. First, it mentions that Picasso entered the school when he was only fourteen, which shows how special it is to be accepted there at such a young age. Also, the description of the school as "well-regarded" suggests that it is highly valued in the art community. These clues help us see that "prestigious" means that the school is important and has a lot of honor.