Why is it dangerous to touch terminals of high voltage capacitor even after applied potential difference has been turned off?

A capacitor is used to store charge. It does this by the means of an electrochemical reaction. After the charging circuit is turned off, this charge - if not discharged by any means - is still present in the capacitor. High-Voltage capacitors can amass sufficient current for it to be lethal at said voltage, and they can deliver all of it at the slightest contact.

For example, a flasher circuit used in a typical photo camera can deliver lethal voltage, even when it's been charged from a 1.5V battery. The current doesn't need to be high (and is typically very low).

I've made this mistake more than once in my life, and I've had screwdrivers welded to the capacitor terminals by their charge. :D

It is worthy of note that some devices and circuits act as capacitors even when they're not designated as such! For example, a Cathode-Ray Tube (the big-ass thing in a tube TV) is a very good high-voltage capacitor itself, and can hold a charge for a long time (even weeks)!