Significance of energy and power signals in real world
I mostly agree with @PeterK.'s answer; in practical terms, all signals are energy signals. However, a signal's energy does have important practical significance. Producing a signal of a given energy consumes at least that same amount of energy, for which you have to pay. In a battery-operated device, this becomes very important, because batteries store energy.

If you're using a signal to communicate, then the more energy it has, the farther it will reach (I'm oversimplifying a bit, but in general this is true). The more energy a signal has when it is received, the easier it is for the receiver to recover the information in the signal without (or with few) errors.

Many devices are also limited in the amount of energy they can produce per unit of time, which limits the kinds of signals they can produce.