Why the compute demand is so large
Training adjusts a very large number of parameters. Each adjustment requires running an input through the model, measuring the error, and correcting the parameters. That cycle repeats many times over the whole dataset, so the total number of simple numerical operations is enormous compared with fitting a traditional model on a modest table.
Why specialized hardware enters the picture
The operations are simple and highly repetitive, and they can be performed many at a time rather than one after another. Graphics processing units, or GPUs, were designed for that pattern of work, so they carry out these repeated operations far faster than a general-purpose processor. Deep learning is therefore not just slower on ordinary hardware; it is often impractical without hardware suited to this kind of parallel repetition.
Data, scale, and compute are linked, not independent. More data helps only if you can afford the compute to learn from it, and a larger model helps only if you have the data to constrain it. That is why the three are usually considered together.
Where traditional methods stay competitive
On a small, well-understood dataset, a traditional model can match or beat a deep model while being faster to build, easier to explain, and free of the compute bill. Deep learning earns its cost when the data is large and unstructured enough that discovering the representations is worth the hardware.