Pique means, among other senses, “to excite (interest, curiosity, etc.),” as in the suspenseful movie trailer piqued my curiosity. The term can also mean “to affect with sharp irritation and resentment, especially by some wound to pride.” This, of course, is another form of excitement, if undesirable.

What does it mean to have your interest piqued?

Pique can still be used (especially in British English) to mean "to arouse anger or resentment in," as in "Their rudeness piqued me." Now, however, it's most often our interest or curiosity that gets piqued—that is to say, our interest or curiosity is aroused: The large key hanging on the wall piqued my curiosity.

Is it piqued my interest or peaked my interest?

The traditional idiom is to pique one's interest, with pique meaning “to provoke or arouse.” Like perk, however, peaked can also make sense in context. Peak means “to bring to a maximum value or intensity,” and this is certainly what one might mean when saying, “my interest was peaked.”