In contrast to the Liked Posts, Disliked Posts, Liked Comments, and Disliked Comments options, which don't appear to work yet, the Hidden Posts option (on both one's own user profile and other user profile) simply displays the contents of the All feed below the user page header.

Edit: Although the 0.4.5.14 update fixed the problem of the hidden posts user profile section appearing on every user profile, rather than just one's own, it still appears to just list the contents of the All feed, rather than specifically posts that the user has set as hidden.