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Think of the universe not as objects flying apart, but as the fabric of space itself stretching. The more distance there is between two objects, the more 'new space' is generated every second, across that entire distance.
Light travels 9.461 × 10^15^ meters per year. At a certain distance (the Hubble limit), more than 9.461 × 10^15^ meters of new space is created in a year. So for stars beyond the Hubble limit, the light sent from those stars actually ends up further from us after a year than when it started. That's what "moving away from us faster than light" means.