What exactly is paradoxical anxiety?

Arises inversely: Paradoxical anxiety is anxiety arising from use of methods or techniques which are normally used to reduce anxiety, such as cognitive behavioral therapy, meditation, medications etc. The most common case would be when taking benzodiazipine medicines such as klonipen which should lull one to sleep but instead causes insomnia or agitation.

Opposite reaction: Paradoxical anxiety usually is referred to as the anxiety one experiences as a side effect of a medication whose purpose is to reduce anxiety.