Difficutly spike means that a certain spot in a game, which can be just a part of a level or a boss, an entire level or multiple levels after another, is much harder than most stuff before or after it.
It's actually possible that one's difficulty spike could actually cause no problem to another player.
Few examples from me:
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Donkey Kong Country - Snow Barrel Blast

That levels starts pretty normal, up to the half point where you suddenly have to shoot the apes through a bunch of barrels, which is much, much harder than anything before and after that. Yes, there is a way to skip all these, but a first-time player without prior knowledge, like me, can just find it by complete accident.
Wario Land 1 - Course 25
I played though this game for the first time today and I lost most lives on this level. Sure, The level after the checkpoint is already quite hard, but then you have to fight a boss, Big Head.

That one right here. I'm sure he's the hardest boss in the whole game, even harder than the final boss. After a short while, he starts to destroy the platforms underneath you and you have to defeat him before he destroys the last one. I lost so many times on him, and I won while there were just two tiny spots left.
Now, your turn.
P.S: Yes, I got that name from TVTropes. You should name your own examples.
It's actually possible that one's difficulty spike could actually cause no problem to another player.
Few examples from me:
----
Donkey Kong Country - Snow Barrel Blast

That levels starts pretty normal, up to the half point where you suddenly have to shoot the apes through a bunch of barrels, which is much, much harder than anything before and after that. Yes, there is a way to skip all these, but a first-time player without prior knowledge, like me, can just find it by complete accident.
Wario Land 1 - Course 25
I played though this game for the first time today and I lost most lives on this level. Sure, The level after the checkpoint is already quite hard, but then you have to fight a boss, Big Head.

That one right here. I'm sure he's the hardest boss in the whole game, even harder than the final boss. After a short while, he starts to destroy the platforms underneath you and you have to defeat him before he destroys the last one. I lost so many times on him, and I won while there were just two tiny spots left.
Now, your turn.
P.S: Yes, I got that name from TVTropes. You should name your own examples.