This applies to Macs, Linux and Unix.
Q: So what does ~/Desktop mean!?
A: The tilde "~" is a short way of saying "the user's home folder". Hence, ~/Desktop means the user's OWN desktop. Similarly, ~/Library would mean the user's OWN Library.
Q: So what is this "Library" you talk about?
A: Well, at least on Macs, the library is the place where all of the user's settings are stored. It's kind of like the registry in Windows, but better (long story).
Q: What do all the slashes mean, "/" and "\" ?
A: On Unix/Linux/Mac the forward slash "/" designates a folder (a directory). On Windows, the backslash "\" designates a folder. So, in Windows, to write down where a folder is, you would use this notation:
C:\Documents and Settings\username\My Documents\My Folder
On Unix/Linux/Mac (I'll call them NIX from now, so when I write NIX, I mean Unix/Linux/Mac), you can write down where a folder is using this notation:
As you may have noticed, the "main" drive in Windows tends to be C:\ -- in NIX, the main drive is just "/" -- So you're thinking "Well, doesn't the forward slash designate a folder". Yup, it does, and when it's in the beginning (like in the example above), or when it's written on its own, it refers to the MAIN folder (also called ROOT folder). The equivalent of the "main" or "root" folder in Windows is C:\
Q: So when you say the ROOT of the drive, what do you mean?
A: I'm referring to the main disk/drive itself. In windows, the root drive is C:\, in NIX we just call it "/"