In my personal experiences with psychedelics, these drugs remove mental heuristics, allowing the mind to think unimpeded by usual thought patterns, simply accepting raw data as it comes in. This was striking in sensory information, if you closed your eyes or just stared at something long enough, you observed incredibly different visual input, geometric patterns, greatly strengthened colors (a strawberry was INCREDIBLY beautiful, I almost felt bad eating such a beautiful entity). There was also an incredible inter-disciplinary thought process, I felt the musical, mathematical, computational, logical, natural, all these parts of my mind mixed together wonderfully.
LSD was much longer lasting, around 12 hours, whereas psilocybin was around 6 hours. Psilocybin enhanced my connection with nature, the flying bugs, a handful of berries, and the plants all around me caused an effusion of love and connection. Whereas with LSD, I felt an extremely powerful visual stimulation, the changing fall leaves were extremely vibrant and beautiful, it was akin to 12 hour, mentally-clear cannabis high. I didn't experience any "flashbacks" per se, there was a positive glow in my mood and thoughts for around 5 days, and the day after LSD I still had lingering effects...I also wonder if I will evermore look at the surface of ponds and lakes differently, they have an incredible dynamism and vitality that I appreciated even more on first trip.
For anyone considering psychedelics, do it thoughtfully and methodically. Read the book mentioned in the parent, practice meditation, explore your mind, and really ensure your mindset ("set") is positive and open. Further, plan to occupy a peaceful, quiet place, hopefully lacking too many strangers/social interaction ("setting"). If set and setting are good, you're in for a wonderful time.