In chess, it is usually advisable to have fewer pawn islands than your opponent. However, while I was watching a youtube video by someone called agadmator chess, he mentioned that multiple pawn islands do have their benefits and I'm trying to understand what kind of benefits or scenarios where multiple pawn islands are an advantageous factor.
Such scenarios arise occasionally in the late endgame. For example, this position is a win for white (LiChess):
[fen "1k6/8/8/7p/P2P2pK/8/8/8 w - - 0 1"]
while a similar position (where white has fewer pawn islands) is a draw (LiChess):
[fen "1k6/8/8/7p/PP4pK/8/8/8 w - - 0 1"]
In the first case, if black's king captures a pawn, the other white pawn promotes (although white needs to play precisely). In the second case, black's king can stop both from promoting because they're closer together, i.e., because of there being one pawn island.
More pawn islands is an endgame disadvantage, even a late endgame disadvantage because it means that the side with more pawn islands has more weaknesses to defend.
The obvious advantage to more pawn islands is where one side has made pawn captures creating doubled pawns and half open files which can be used for an attack. These can give a temporary advantage through the late opening and middlegame but later turn in to an endgame disadvantage if the player does not turn his dynamic advantage into either a win or a static advantage.
Such a position can even be an early endgame advantage if it allows fast activation of one or more rooks.
In general there are lots of rules from the time of Nimzowitsch's "My System" which have proved in modern times to be too inflexible. There is an excellent book by John Watson called "Secrets of Modern Chess Strategy: Advances since Nimzowitsch" which reassesses these positional ideas.
I guess one case would be the outside passed pawn in a pawn endgame. i.e. if white has two kingside pawns and an a-pawn, and black has three kingside pawns. In that situation white will be winning usually.
I wouldn't really think about pawn islands there though - it's a useful paradigm for evaluating pawn structures but it's not the only one.