I have had always heard the experience referred to as "dreamwalking"
It works both ways, but my understanding has always been that it takes an incredibly strong will to call someone into a dream of your own.
However, it basically works like this......
Through stresses caused by a nightmare or through the stresses caused by someone elses nightmare.....or by sheer will....you actually project yourself
into someone elses dream, or you respond to a psychic request by someone to help/be with them in theirs.
I have only done it a very few times in my years, but all those times involved nightmares of either myself or the other party.
When I was younger and living at home with my
parents, I used to go into my mothers dreams
a lot. She and I would have the same dreams and
we would be in each others dreams when they were
the same. This stopped when I moved out of the
house when I turned 19.