Furthermore, Cloud marks Zack's place of death (just outside Midgar) in the Advent Children trailer through the Japanese ritual (far as I know) of sticking a sword into the ground at the place of a soldier's death.
As for the connection - Zack was a role model to Cloud who was frankly a bit of a failure. When exposed to the mako capsule, Cloud lost his mind and needed something to grasp onto - when Zack died, his personality was that 'thing' to grasp and somehow he became almost the same person, even adopting his memories.
What they have in common is Aeris - Zack was her first boyfriend. That's why she fell in love with Cloud, the resemblance of Zack. But those were probably for the wrong reasons.... it does however explain why she asked to "meet YOU".
They also both new Tifa, but as far as I know Zack only met her briefly on the mission and nothing more.