An external reference is just that--a copy of another (external) drawing that you include (reference) in your current drawing. The XREF is read-only; you can't change it unless you open the original file. It's sort of like projecting the other drawing onto a wall and taping up your drawing so they overlap.
The big advantages of XREFs are keeping drawings at manageable sizes, since you can split one big project into different parts, and allowing multiple people to work on one project at the same time. The disadvantages are complexity, since you have to keep track of which things go into which drawings, and having to keep track of where the drawings themselves are.
It's possible to BIND an XREF into your drawing. Instead of referencing the other drawing, you bring it into your drawing. The problem with doing that is, you've made a copy of the other drawing, a copy that has no connection to the original. After that point, if someone updates the original, the changes won't be reflected in your drawing.
An overlay is a standard XREF. An attachment is the same as a bound XREF, you get a copy. An underlay is not a drawing but a PDF, DWF, or other type of file.