As other answers have said, dots are used to represent a hierarchy, just as / or \ is used to represent a filesystem hierarchy.
Placing widgets in a hierarchy is not, strictly speaking, necessary. One advantage in doing so is that geometry managers such as grid and pack default to managing children in their parents. For example 'pack .a.b.c' will pack the widget a.b.c within the widget .a.b. This makes it easy to do simple layouts.
The same effect in many cases can be achieved by telling grid and pack into which container a child should be placed. Foe example, 'pack .c -in .a.b' will put the widget .c in the container .a.b. This let's you keep your hierarchy shallow, and makes refactoring a little easier.
See http://www.beedub.com/book/2nd/TKINTRO.doc.html for a good introduction to tk fundamentals.