Pique is a French word, meaning "to prick, sting, or pierce."
So if something piques your interest, it gets your attention in a way you just can't ignore. When your interest is piqued, you want to follow up and learn more about whatever excited you, as in these examples:
Seeing a show at Radio City Music Hall piqued her interest in becoming a stage performer. (Washington Post)
She was always eager to delve deeply into whatever piqued her interest, everything from photography to Latin. (The Boys in the Boat)
A peak is the top of a mountain or the highest point of something, like a graph or even a hat. As a verb, to peak means "to reach the highest point." So you might say that Pokémon Go initially piqued your interest during the fall of 2016, but that your enthusiasm for the game peaked during the summer of 2017, when you spent hours playing every day.
Because peak means the top, the maximum, it's possible to understand how people, even professional writers, confuse it with pique, as in the following examples:
Revealing this new information to the police peaks their interest and now paints Shaw as a person of interest in Sophie's disappearance. (Washington Times)
Sharon said he comes across many people who don't think opera is for them, but he hopes hearing about these kinds of "audacious experiments" will peak their interest. (Time)
Just remember that the phrase pique my interest isn't talking about the moment when your excitement about something peaks, or reaches its high point. Instead, it refers to the moment when something grabs your attention and spurs your curiosity.