The story of the game is not explained within the game and is directly taken from a SCP entry with the same name, SCP-087.
In SCP-087 there is no clear objective and the only thing that you can do is walk. The game is randomized and as the player walks down the staircase it is possible to encounter a threat at any moment.
There are other versions of SCP-087. The core gameplay is the same but encounters and setting are different.
SCP-087 is the original and consists of only a staircase.
SCP-087-B has the setting of hallways.
SCP-087-C Is called the circus
SCP-087-G Is a comedic spin-off where the antagonist is Gabe Newell
This is the story from which the game is based from