The Apocalypse is the sequence and events of the final days, the end of the world as we know it, etc. The Supernatural universe, drawing on Christian tradition, focuses on the seals that need to be broken for the Apocalypse to begin in earnest.
The seals we have seen and heard of involve various ritual atrocities and negative events. Bobby mentions a species going extinct, a school teacher killing exactly 66 children, and an entire fishing boat crew being struck blind as seals.
Now that Lucifer is free, the Apocalypse is supposed to really get into gear.