A psychedelic is any substance that produces a profoundly altered state of consciousness, and a sense of expansion of perception. They typically (but not always) work by affecting the serotonin system in the brain, but most importantly can induce mystical or spiritual experiences in those who take them.
Psychedelics can include both plant medicines (like ayahuasca or peyote) and synthetic substances (like LSD and ketamine). Arguably, any substance that can evoke profound changes in consciousness could potentially be grouped psychedelics – such as cannabis and MDMA.
The common factor with all psychedelics is their power to show people a very different way of seeing the world, and their potential to catalyze profound personal transformation.