There is no significance other than past practice, enabling the faithful of the parish to offer their financial stewardship in support of their parish's mission. Typically, a second tray was for a special fund, like the Building Fund or a mortgage, the first tray being for the parish's operational fund.
Is passing a tray something from the West or North America that we adopted?
My parish adopted passing one tray since its inception in 1966, except for Christmas, Palm Sunday, Great Friday evening, and Pascha. Each second tray had a designated purpose, the Christmas 2nd tray was for the Benevolent Fund. After two priestly tenures over a 42 year period, our current presiding priest eliminated the 2nd tray all together and revenue has not been affected. (Some of the logic behind the 2nd tray was hitting up people who come to church only on those holidays. Others criticised the practice indicating you'd only come to church on holiday's too if you got hit up for donations as much as we do on those days.)
A parish in my area eliminated passing a tray altogether for a few years, years ago, opting to have a tray stand in the narthex, and their revenue was substantially reduced, though, many in that church were opposed to the change and reduced their own contributions to demonstrate their opposition to not passing a tray.