The Reset vault allows you to store seasonal items (select a few other items, tags, heads, etc ) throughout resets. They open a select time after the reset happens and allow you to remove ONLY items in that period. Then, towards the end of the season, you are allowed to add items to the reset vault. Once added, they can not be removed until it opens again the next season.
During a reset, everything is wiped (on that server) besides ranks, gc, and what is in reset vaults (and what is global/across the network/other game modes, so tags, etc)
GC means gift card; it is bought at the complex store and can be used to trade with players in the game or buy items/ranks on the complex store. It works as the complex's primary system and carries over to all game modes on the complex (besides pixelmon, but it can be converted to gems).1gc = 1 $.
The goal of Skyblock is the gain more and more eco and do the personal and island milestones. You can make a comp island or just a normal island. Most players who make normal islands try to do their milestones. Milestones allow you to leave your island and access other milestones. Milestones give rewards, and if you complete all of your milestones, you get a tag. Those who make comp islands try to compete for the island top; basically, who makes the eco (it's a bit more complicated, just that's the gist).
Not sure when the next reset is; but it's generally when it gets stale or boring, determined by staff (usually once per 7-9 months on skyblock).