By Tim Kralj

A question of a fair bit of scholarly debate.
He is usually, as the other answer says, portrayed as the son of Zeus in mythology.
This does not however exclude the possibility, that there may have been a historical person at one point, that had a lot of stories writen around him.

There were historical personalities like that; king Arthur is a nice example; most likely a british leader that led the defense against Saxons in the late 5th and early 6th century. Most likely a real person. Definitely didn’t have a magical sword called excallibur that he pulled from the rock to become king, wasn’t raised by a wizard, didn’t have a round table and twelve knights, pretty much everything the story is known for today - all things were later medieval additions to the story.
The case of king Arthur is interesting here, because it shows us just how much can get added to a specific story over time.

Another thing to note is, that there are a lot of interesting speculations about the potential origins of different stories about Hercules.
Capturing the Cretan bull is likely an allegory of some kind of a successful military incursion against Crete.
Fighting the hydra may refer to an attempt to drain a swamp - closing off one stream of water may open several others elswhere, there are poisonous gasses, crabs bitting you, central stream of water (a river) impossible to shut off.

There is the story of a fight between Hercules and a river god Achelous for the hand of Dejanira; short version, the river god shapeshifted a few times, while he was in bull form Hercules broke off his horn and it became the legendary “horn of plenty”, Hercules won the endavour.
Bulfinch in Bulfinch’s mythology gives us the following explanation:

“The ancients were fond of finding a hidden meaning in their mythological tales. They explain this fight of Achelous with Hercules by saying Achelous was a river that in seasons of rain overflowed its banks. When the fable says that Achelous loved Dejanira, and sought a union with her, the meaning is that the river in its windings flowed through part of Dejanira's kingdom. It was said to take the form of a snake because of its winding, and of a bull because it made a brawling or roaring in its course. When the river swelled, it made itself another channel. Thus its head was horned. Hercules prevented the return of these periodical overflows by embankments and canals; and therefore he was said to have vanquished the river-god and cut off his horn. Finally, the lands formerly subject to overflow, but now redeemed, became very fertile, and this is meant by the horn of plenty.”

And it should be noted that it is not unheard of, that the deeds of several people (or stories derived from deeds of many historic people) could get attributed to a single protagonist that may have only participated in a fraction of them.

But perhaps the most interesting part of the stories of Hercules is the stories about his son Hyllus.
You won’t find it in most mythology books, and there’s a good reason for that: they seem quite lame compared to the deeds of Hercules.

I’ll just copy paste a version of it from wikipedia:

“Heracles, whom Zeus had originally intended to be ruler of Argos, Lacedaemon and Messenian Pylos, had been supplanted by the cunning of Hera, and his intended possessions had fallen into the hands of Eurystheus, king of Mycenae. After the death of Heracles, his children, after many wanderings, found refuge from Eurystheus at Athens. Eurystheus, on his demand for their surrender being refused, attacked Athens, but was defeated and slain.

Hyllus and his brothers invaded Peloponnesus, but after a year's stay were forced by a pestilence to quit. They withdrew to Thessaly, where Aegimius, the mythical ancestor of the Dorians, whom Heracles had assisted in war against the Lapidae, adopted Hyllus and made over to him a third part of his territory. After the death of Aegimius, his two sons, Pamphylus and Dymas, voluntarily submitted to Hyllus (who was, according to the Dorian tradition in Herodotus V. 72, really an Achaean), who thus became ruler of the Dorians, the three branches of that race being named after these three heroes. Being desirous of reconquering his paternal inheritance, Hyllus consulted the Delphic oracle, which told him to wait for "the third fruit," and then enter Peloponnesus by "a narrow passage by sea."

Accordingly, after three years, Hyllus marched across the isthmus of Corinth to attack Atreus, the successor of Eurystheus, but was slain in single combat by Echemus, king of Tegea. Heracles, whom Zeus had originally intended to be ruler of Argos, Lacedaemon and Messenian Pylos, had been supplanted by the cunning of Hera, and his intended possessions had fallen into the hands of Eurystheus, king of Mycenae. After the death of Heracles, his children, after many wanderings, found refuge from Eurystheus at Athens. Eurystheus, on his demand for their surrender being refused, attacked Athens, but was defeated and slain.

Hyllus and his brothers invaded Peloponnesus, but after a year's stay were forced by a pestilence to quit. They withdrew to Thessaly, where Aegimius, the mythical ancestor of the Dorians, whom Heracles had assisted in war against the Lapidae, adopted Hyllus and made over to him a third part of his territory. After the death of Aegimius, his two sons, Pamphylus and Dymas, voluntarily submitted to Hyllus (who was, according to the Dorian tradition in Herodotus V. 72, really an Achaean), who thus became ruler of the Dorians, the three branches of that race being named after these three heroes. Being desirous of reconquering his paternal inheritance, Hyllus consulted the Delphic oracle, which told him to wait for "the third fruit," and then enter Peloponnesus by "a narrow passage by sea."

Accordingly, after three years, Hyllus marched across the isthmus of Corinth to attack Atreus, the successor of Eurystheus, but was slain in single combat by Echemus, king of Tegea. ”

And the story then goes on, to explain what his descendants did, etc.
What really strikes me as interesting here is though, is the change of tone. No more legendary monsters, mundane problems like pestilence stopping Hyllus from his goals, really the whole thing feels more like someone writing down history for the sake of writing than history, rather than some epic retelling of the awesomeness of Herculess to impress audiences. Where the story of Hercules could be an impressive peace of entertainment and propaganda, I can see very little reason for any authors to lie in the story of Hyllus.
Some details look exagerated; there’s basically a tragedy thrown during the siege of Athens by Eurystheus, and I can imagine why a writer of tragedies like Euripides might decide to throw in a story like that, even if he has to make it up altogether. But by and large,most of the story looks kinda legit; it seems to me to defy any literary conventions to much to be just a piece of fiction.

But at the end of the day, all we have are remnants of the stories that got preserved for more than 3.000 years. So ultimately, unless we find some remarkable new evidence (though I can’t quite immagine what kind of evidence would even clear this up) we’ll probably never know the truth and we’ll just be left with speculations like this post.