DC/AC coupling in an oscilloscope
DC coupling shows you the whole signal, and AC coupling shows you only the AC component.  Since these are different, it should be no surprise that each has its own advantages and disadvantages.

A basic example of DC coupling is to see the voltage of a power supply.  Digital signals usually make more sense when viewed with DC intact.  A signal may stay high for a long time, then start toggling a lot.  The average DC will then go from the power supply level to about half that.  Seeing the signal appear to float down during that time is misleading.

A basic example of AC coupling is to see the ripple on a power supply.  The supply may look like a flat line at 3.3 V with DC coupling.  If you try to crank up the gain to look at the ripple, the trace will be off the screen.  AC coupling removes the average DC bias and lets you amplify only the deviations from that average.  With AC coupling, you can crank the gain to 10 mV per division and see the level of noise, the pulses from the switching supply, or etc.