A beholder is an observer: someone who gains awareness of things through the senses, especially sight. If beauty is in the eye of the beholder, then the person who is observing gets to decide what is beautiful.
A common saying is "Beauty is in the eye of the beholder," which means beauty doesn't exist on its own but is created by observers. That famous quote can help you remember that a beholder is someone who sees or otherwise experiences things, becoming aware of them. To be a beholder, you have to pay attention. Different beholders might take in different aspects of the same event, like witnesses to a crime.