The idea is to keep everything around the device at the same potential. Thus in a lab/production environment they use anti-static bench pads and wrist-straps connected to a common (typically earth ground) point. All containers and bags should also be of an anti-static (conductive) design. Normal plastic materials (bags and containers) are bad since they can develop a high electro-static charge.
You can't assign a percent of danger, but all it takes is one small electrostatic discharge (one you wouldn't even feel) to kill many MOS devices (which normally take only a few tens of volts to puncture the gate dielectric). For example, walking across a carpeted floor and touching a sensitive device would likely zap it.
You must always ground yourself and the device before touching it. A typical procedure would be to ground yourself with a connected wrist strap, then pick up the electro-static bag with the sensitive part inside. That puts you and the part at the same potential so it's now safe to open the bag an remove the part. Wherever you place or install the part should also be grounded to the same potential.
Typically all connections to earth ground are made through a 1 megohm resistor for safety reasons.