The Hypercube is what links you to the chaos caused by the Event. It's the aftermath of the disaster that keeps sucking things in and dismantling everything in its path. Don't worry about the weird colors on your screen! It's just the kingdom of chaos opening its gates.
Random Models that need to be built within a certain amount of time can be recovered from the Hypercube. If you fail to do so, the Model will be lost and may never be seen again. Where the Hypercube leads to, nobody knows.
If the Model is completed on time, it goes to the Bag and you receive a capsule as a reward.