the twenty three simple rules of happiness
Zack was known to be a "ladies man", Aerith says so herself if you visit Zack's parents in Gongaga while she's in your party. Zack was popular among the ladies, he was strong, he was honorable, he was young, he was cute, and as far as most knew, he was single. Shinra's female workers even had a fan club to Zack with pictures and everything. Zack could have had any girl he wanted but the one he chose was Aerith Gainsborough. He met her when he fell through the ceiling of her church (not unlike another Final Fantasy VII hero). She was a slum girl whose ability to speak to the planet kept her under constant surveillance by the TURKS.
Zack immediately hit it off with her. She was bright, outgoing, and wise beyond her years which made her a perfect match for Zack's bright, outgoing, and impulsive nature. They were able to share the same strengths while countering each other's weaknesses. They quickly became a couple and Zack would visit her in the slums. Aerith always seemed to be able to make things better when Zack was depressed about his duties or the loss of his friends and Zack was able to help Aerith overcome her fear of SOLDIERs and the sky. Before Zack left for Nibelheim Aerith told him about Twenty Three simple pleasures, the most important to her was to spend time with him. Unfortunately, they never got the chance to spend time again.
When Zack awoke in the Shinra Mansion his first thought was safety. He wanted to get away from Shinra altogether. He reached in his pocket and saw Aerith's note "twenty-three", their promise to spend more time together. He knew he had to return to her. As he tracked across Gaia she was the thought most prevalent in his mind, returning to her. Aerith had not forgotten about Zack either, she had written him a total of 89 times in the four years apart; she missed and prayed for his return. He never did come back to her but he died with his memories of her prevalent in his mind.
Aerith undoubtedly made an impression on Zack and from the moment they met, she seemed to be the center of his world. There weren't many scenes of them together, but over everyone else who Zack met, she was the one who stayed in his mind until the end. She was his driving force and the reason why he was so desperate to return to Midgar. He had promised he'd come home to her and he wanted to keep it no matter how long it would take. I think Zack felt that Aerith completed him. Even if their relationship wasn't the most romantic (at least in the classic sense) she was able to help him out by thinking of things he never could and she always put a smile on his face.
Zack meant to the world to Aerith as well, which is why she originally shows interest Cloud. Cloud reminds her of Zack in every way possible. They both fall through the roof of her church, they both take her to have a deep heart to heart to the playground, and they were both "members" of SOLDIER. That being said, I'm not saying that Aerith didn't eventually grow to feel for Cloud as an individual, but I believe that their relationship stemmed from the similarities he shared with Zack. I think the reason Aerith treasured Zack so much was because he wasn't cold like the TURKS who had always followed her or ruthless like the SOLDIERs she imagined. He was able to make her believe she could overcome anything. He was always motivated to get her to try new things or coming up with new ideas (like selling flowers) and he would put a smile on her face as well.
After Aerith joined Zack in the lifestream, I feel like they had lost the romance they had previously shared. I believe that Aerith grew a lot during her journey with AVALANCHE and it led her to grow apart from Zack. After her death Aerith's actions where always meant to help Cloud. I think that Zack, who hadn't had the time to live without Aerith was forced to realize how much she had changed when he reunited with her in the lifestream. In Hoshi wo Meguru Otome, Aerith tells Zack that she's changed and that his kindness to everyone makes him less attractive than Cloud. I think that Zack is happy for Cloud to have finally found someone and he helps her take care of Cloud by joining her as one of his guardian angels. Zack never showed any signs of jealousy towards Cloud even though he stole Zack's girlfriend. I think that as much as he loved Aerith, he wanted both her and Cloud to be happy, even if they could never be together.