What is this plant?

Update - the plant appears to be Disocactus flagelliformis, also called Rat Tail Cactus. I'm not 100% certain that's what it is but I think that's correct.

Someone in our office suite gave me this cactus because it was in their way and they were tired of bumping into it. It's a neat looking plant, I think, but we've had a few customers walk in and say something like, "Oh! Your cactus freaked me out!!"

I'm not sure how to care for it. Some of it is green and some is brown. I don't know if it needs water or if it's supposed to look like that.

Just what is this thing?





I moved it outside for awhile and got another picture.



And here's one of new growth



If you have an idea what it is and how to care for it, please let me know. I want to give it a great home.