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Everyone in the wizarding world is born with a soul mark on their forearm. The mark is revered and treasured. The soul mark matches that of a soul mate, the one you are meant to be with forever. Most wizards hide them until they reach maturity to allow for organic meetings and relationships to grow.
The Dursleys burned Harry's soul mark off when he was little. He grows up thinking he is too much of a freak to have one. He eventually learns that despite everything, he should have a soul mate, but probably doesn't deserve one. He thought he would never reach maturity because of the war. All he was worth was a weapon forged to kill the enemy. He would not live to see past the end of the war. The soul mate issue wouldn't even matter then.
When Harry survived the war, he was surprised. He was angry and depressed. What would his life be like now that the war was over? He had no reason to go on. There would be no match for him. Sure, logically his match was out there somewhere, but he would never know if they were his true match. Those who claimed to have a match to Harry's mark usually just wanted to have a match to the-boy-who-lived.
The only thing that kept Harry going was his job. He had become an Auror after the war. Mostly to catch the last of the Death Eaters. He didn't know what else to do. It seemed like there was no other option for Harry. He also wanted to help Kingsley.
Ron was his partner for a few years before leaving to work with George in Weasley's Wizard Wheezes. Harry gained a new partner in Draco Malfoy of all people.
Working with Draco was great. He was Harry's equal. He challenged Harry and complimented Harry. He evened Harry out. He even helped when Harry was stressed out. Draco also made sure to keep Harry's self-sacrificing to a minimum. It was easy to become friends with him. It was even easier to fall in love with him.
Harry was brought up short when he realized he was in love with his partner. He had to forcibly look away and remind himself that he wasn't worthy of a soul mark. Draco had a soul mate, and it wasn't Harry. So, Harry kept his unrequited feelings to himself.
Harry would often go home and look at his scarred arm (which he kept hidden) and rub over it while daydreaming of it healing so he could find his match. He usually ended up crying himself to sleep when he did. When he started fantasizing that his match was Draco, he knew this would have to stop. He just didn't know how.
When the appointment for the new Head Auror was up, Harry was relieved to be appointed. It meant that he could put space between himself and Draco. He could keep the professional relationship he had with Draco.
As the years passed, the stronger Harry became. The more Harry was able to deal with his missing soul mate. He still longed for them but was happy without them. Or at least as happy as he could be. He went on to become the best Head Auror the Ministry ever had. He still visited his friends and had a decent life outside of work.
He was finally okay with being burnt.
THE END