Who is the "hero" in A Hero of Our Time? What makes this person heroic?

In this Russian classic, the hero is Grigori Aleksandrovich Pechorin. He is what we would call an antihero or Byronic hero, in the vein of Robert Lovelace from the novel Clarissa or Edward Rochester from Jane Eyre. Modern examples of antiheroes or Byronic heroes include Clint Eastwood in the Good, the Bad, and the Ugly and Dexter Morgan in the TV series Dexter. Eastwood and Morgan portray iconoclastic heroes who are flawed but hold to personal codes of honor.
Essentially, antiheroes fascinate us because they are relatable and oddly likable. Take Dexter, for example. He may be a cold-blooded murderer, but he only executes serial killers, rapists, and pedophiles.
In A Hero of our Time, Pechorin is the ultimate antihero. He's a self-absorbed, debauched sinner who delights in jilting the women he has seduced (such as Bela, Vera, and the Princess Mary). Pechorin has none of the typical attributes we would expect in a hero. He is neither moral nor selfless. Instead, he's a cynical loner and an unabashed nonconformist. Yet, he captures our imagination because he delights in defying social conventions, and he does so with little guilt. He is a hero because he remains intractable in the face of societal pressure to conform.
Maksim Maksimych, one of the novel's narrators, documents Pechorin's larger-than-life character:

He was a splendid fellow, I can assure you, but a little peculiar. Why, to give you an instance, one time he would stay out hunting the whole day, in the rain and cold; the others would all be frozen through and tired out, but he wouldn’t mind either cold or fatigue... I myself have seen him attack a boar single-handed. Often enough you couldn’t drag a word out of him for hours together; but then, on the other hand, sometimes, when he started telling stories, you would split your sides with laughing.

Here, Pechorin is portrayed as a maverick who socializes according to his own terms. He can be an extremely pleasant companion when it suits him. At other times, he can be dismissive, cold, and even cruel. However, Pechorin is also unequivocally rugged and appears to be physically superior to the men he hunts with. Although we are repulsed by Pechorin's contemptible self-absorption, we admire his physical prowess and inner strength. Like all heroes, Pechorin is his own man; he is strong, self-sufficient, and content to stand alone. He freely admits his faults, but we admire him all the more for his honesty.

Mine is an unfortunate disposition; whether it is the result of my upbringing or whether it is innate—I know not. I only know this, that if I am the cause of unhappiness in others I myself am no less unhappy...

Pechorin may be a self-absorbed antihero, but he still earns our admiration. Why? Despite his obvious flaws, Pechorin speaks to our innate desire to live life on our own terms. Additionally, his outward physical strength, coupled with his self-sufficiency, makes him an undeniably heroic character.