It's been many hours since I raised a flag on Why is this inequality true in this proof?. Any guesses why it's still showing "active"?
As Mad Scientist pointed out in his answer, there are many reasons why flags are not handled on immediately. In addition, flags that point to some behavior of a user we should watch out for will usually not be cleared very soon, if we agree that the behavior is worth watching out for but does not yet call for immediate action.
The average flag takes much more time to handle than the median flag. Things like proper insults, spam etc will usually be killed off very fast.
There are a few reasons why flag handling might take a bit longer:
No moderator is online currently. This is a rather big factor on sites with fewer mods and with a heavy timezone bias. Moderators don't handle flags when they are sleeping.
There are a lot of flags in the queue and relatively few moderators online at the time. MSE has a rather high question volume now, I wouldn't be surprised if the flag queue reached triple digits (though I don't have any internal data).
A moderator or several looked at the flag, but were not sure what to do about it.
A moderator looked at it, but dealing with the issue requires more time and the flag is left as a reminder. For example, if you flag a case of suspected vote fraud it might take a bit longer to deal with.
Then there are also flags that don't go through the moderators, specifically close flags which are handled by the community in the review queue now.