What does this scene mean?!

The one Shige is "hiding" is a propaganda poster of some elections candidate - covering up with something else may be considered a serious offence (as you were trying to "sabotage" this candidate).

Also the board looks like one exclusively reserved for elections candidate posters.
Actually covering a poster would be like adding insult to injury, hence the speechless policeman.

I thought the subtitled version was pretty clear on this - the policemaan told the grandma she couldn;t put her poster there because the board was RESERVEd for election candidates. naturally,he was speechless when he saw she'd actually covered one of the posters. I haven't seen the dub, may they left this bit out altogether from the Eng soundtrack.

Nope, you're not the only one. I didn't get that either. Like most people used to Hollywood movies where situations to laugh at are signposted, I simply didn't see it's not WHAT she's covering, it's the fact that she is COVERING. Thanks to all those who took the effort to explain.

Also one of the reasons for the policeman to be speechless could be the fact that most of the board was empty and she decided to put her poster over another one.