Short Answer:
A type of Gibson Custom Shop Les Paul guitar based off vintage Les Pauls featured in Yasuhiko Iwanade's 1996 photography book, The Beauty of the 'Burst.
Long Answer:
Back in the '90s, photographer Yasuhiko Iwanade published his book, The Beauty of the 'Burst. This book focused on capturing the aesthetics and experiences of Gibson Les Paul guitars which, even at the time of photographing in the 1990s, were solidly vintage. Iwanade assembled a vast lineup of Les Pauls ranging in production from 1958 to 1960 for his book. At the time, this span of years was seen as a golden era creatively and technically for Gibson. Thus, models from the years of 1958 to 1960 are still highly coveted for collectors globally.
Today's Gibson Custom "Beauty of the 'Burst" take direct inspiration from specific models depicted on specific pages of Iwanade's The Beauty of the Burst. This method drives Gibson Custom Shop "Beauty of the Burst" models to be marketed commonly with accompanying page numbers in their titles. For instance, a Gibson Custom "Beauty of the 'Burst" Les Paul model might be listed with "Page 40" in its description to allude to its direct inspiration, the model depicted on page forty of the actual book of The Beauty of the 'Burst.
Gibson Custom "Beauty of the 'Burst" Les Paul models universally make for excellent representations of vintage Les Paul guitars. Whichever "page" of "Beauty of the 'Burst" model you turn to, you're in for an authentic and reverent guitar.