Consider a TTL square wave from 0V to 5V.
If you use the DC setting, the display will correctly show 0 to +5V.
If you use the AC setting, the display will incorrectly show -2.5V to +2.5V
HOWEVER
Let's say you're probing the RF stages of a superheterodyne radio. In this case, there are probably all sorts of DC bias voltages everywhere that you want to ignore, because you're interested in the AC signals only. Signals might be varying from 5.13V to 5.15V in one section, and 9.13V to 9.15V in another.
In this case, AC setting on the oscilloscope is extremely useful. It eliminates the 5V and 9V DC component and allows you to see the 0.03V to 0.05V signal (which will be displayed as -0.1V to 0.1V when AC setting is used).
I'm sure others will chime in with different use cases.