It used to mean someone who literally destroyed icons— as in statues and things that folks would worship.

Nowadays it mostly refers to “A person who attacks cherished beliefs or institutions”. [1]

It connotes that someone isn’t afraid to loudly voice a (potentially) minority or unpopular opinion. See also ‘shit-stirrer’, ‘skeptic’.

It’s also in the title of a classic Simpsons episode. [2]

[1] https://www.lexico.com/en/definition/iconoclast

[2] https://en.wikipedia.org/wiki/Lisa_the_Iconoclast