How does viscous damper work in high-rise buildings?

Answer 1

Are you talking about dampers for earthquake resistance where flexing of building frame is damped?

Viscous dampers normally have a piston which forces viscous oil through small holes.

Answer 2

In vibrations analysis, one can apply an oscillating load of a certain critical frequency to an undamped system and cause catastrophic failure with a very small load magnitude. Damping the system significantly lessens this vulnerability because this key frequency changes with load magnitude once it's damped.