Dreams come with a variety of extraordinary possibilities. Many people are attracted by the possibilitty of being aware that you're dreaming while dreaming. This is also known as lucid dreaming. Knowing that you are dreaming can make the experience very vivid and also gives you more more awareness to decide what you want to do with a dream.
To a large extent, a dream is truly your dream, so you get to decide what happens. You can for example face your monsters in the dream, because you know it is a dream. Nothing bad can happen. You can also try out all kinds of fantasies or creative ideas. Many people for example love to fly in dreams.
The ability to make more conscious decisions about what happens in a dream attracts many people to lucid dreaming. However, about half of the lucid dreamers do not change the dream, but let the dream unroll on its own and meanwhile just enjoy the brighter state of awareness.
Mystics say we are all connected. This can easily be seen in dreams. People who share and compare their dreams, often discover that remarkable similarities show up. The most obvious example would be fully identical dreams, or dreams where dreamers meet each other. More common however are dreams where you will see some object or situation show up that more or less seems to fit in with everyone's dream, but when you think about it, does not fit with the main theme of the dream. In other words, it is as if somehow something was injected into the dreams.
There's no standard terminology for this yet. On Dreamers United the term sync is used. Sync is short for synchroniticy, a term for a meaningful coincidence. It seems the most versatile term that covers the whole variety of dreams that are alike, as well as dreams that resemble daytime events of other people. That's however another topic.
Other terms used for this kind of dreams are mutual dreams or shared dreams. A dream where people meet each other has been called a meeting dream. You could also make the point that some dreams seem to be co-created, even though the term co-creation has gone out of fashion.