What they’re showing is an idealized dual-supply, or bipolar amplifier. Bipolar amplifiers have the ability to both accept and output signals that swing above and below the ground reference. This is made possible by the dual supply, which allows both positive and negative biasing. This is the classic style of op-amp powering, going back to the 1960s and parts like the uA709 and uA741, which are designed to run on +/-15V supplies.
(Note: confusingly, bipolar power is a separate concept from bipolar transistors.)
The alternative is the single-ended or single-supply amplifier. These will usually use GND as the negative amplifier supply. Thus, they limit their input and output swings to be between GND and the positive supply as there is only positive bias available. The LM324 is a well-known example of a single-supply op-amp, although it too can use a bipolar supply.
(Second Note: if you’re talking about real op-amps, review their data sheets carefully and observe their limits: their I/O voltage ranges will usually be less than the supply rails. On the other hand, also note that there are specialty op-amps that can accept wider input voltages, e.g., op-amps designed for high-side current sensing.)
Which kind of powering you would choose depends on kinds of signals you’re processing and your desire for low system cost:
If your signals are always above ground you would choose single-ended for lower cost. This is common for signal buffers to microcontrollers for example.
If your signals are bipolar AC (like audio), you can still use single-ended, with the addition of an artificial midpoint bias reference and AC coupling. Most portable audio electronics are built this way.
If your signals are very low frequency or DC (and thus can’t use AC coupling) and swing above and below ground, using bipolar supplies solves a lot of problems, at the expense of a separate negative supply. You often see this in instrument signal blocks, in high-end audio, and sometimes for high-power servo drives.
Finally, if your signals have a large swing, using bipolar allows for handling a greater voltage range. A uA741 powered with +/-15V can easily handle +/-10V signals.
That all said, textbooks tend to assume bipolar amplifier supplies because it simplifies input and feedback network analysis: they don’t have to consider the influence of an artificial midpoint bias.