One of the first things that Hardy wants us to know about Gabriel Oak is that he's a solid young man and that he's available. Or, "In short he was twenty-eight and a bachelor" (1.5). And if you were a Victorian reader you would be pretty sure that Oak's single status was going to have something to do with how events play out in the rest of this book.
Unlike many single men in novels, Oak doesn't spend all his days moping around and wishing he had someone to be with. Instead, he just tends to his business as a farmer (and later as a shepherd) as well as he can. As the narrator tells us, "on working days he was a young man of sound judgment, easy motions, proper dress and general good character. On Sundays he was a man of misty views, rather given to postponing, and hampered by his best clothes and corpulent umbrella" (1.2). The fact that Gabriel Oak is held down by his best clothes and big umbrella tells us two key things about him: one, that he's not in his element when he's wearing fancy clothes, and two, he cares quite a bit about his appearance in front of others.
The thing that characterizes Gabriel Oak most consistently in this book is the quiet, dignified way he goes about his life, no matter how many terrible things happen to him. This calmness allows Gabriel to quietly appreciate a lot of things in life that other characters don't. For example, "Being a man not without frequent consciousness that there was some charm in this life he led, he stood still after looking at the sky as a useful instrument, and regarded it in an appreciative spirit, as a work of art superlatively beautiful" (2.19). He may just be a farmer and shepherd, but Oak still appreciates the fact that his work keeps him in contact with nature, and he finds peace in this.
Even when Gabriel's sheep fall off a cliff and lead him into total bankruptcy, the guy doesn't go nuts and start cursing God. Instead, we find out that "there was left to him a dignified calm he had never before known and that indifference to fate which, though it often makes a villain of a man is the basis of his sublimity when it does not" (6.5). The narrator tells us that most people would be turned into villains by Oak's bad luck, but not Oak. He just draws strength (oak-like strength) from his experiences and keeps pushing onward.
If there's one thing that really sets Oak apart from the other characters in this book, it's his loyalty to Bathsheba Everdene. Even when Bathsheba rejects his first marriage proposal, he claims, "I shall do one thing in this life—one thing certain—that is, love you, and long for you, and keep wanting you till I die" (4.65). But unlike Farmer Boldwood or Sergeant Troy, Oak is not one to keep pestering Bathsheba with proposals until she relents. He has too much dignity to do that sort of thing, and besides, he doesn't want Bathsheba to marry him if she doesn't love him.
To show his commitment to Bathsheba, Oak brings her "in his arms a new-born lamb" (2.13) in the hopes that she will raise it. It doesn't take a huge leap to think of this lamb as a symbolic child, signifying Oak's wish to be married someday to Bathsheba. But the funny thing is that for most of this book, Oak totally keeps his love for Bathsheba on the downlow. It's only at the end when Bathsheba begs him not to leave her that he makes good on his earlier promise and tells her he still loves her. Without question, if there's a moral center to this book, it's definitely Gabriel Oak.