
Drag and overlap is about taking your understanding of Basic Physics and applying it to things that are connected in some way. So if two objects in a scene are moving and are physically connected is one pushing or dragging the other? Is one heavy and the other light? Is the connection between them rigid or flexible?
Understanding how these different factors affect your animation and how to depict them is the art of animating drag and overlap.
Its worth noting that things like Drag and Overlap are often added late in the animation process as part of the Polishing process. But even so it is worth having a basic understanding of the principle at an early stage so that you can visualize how your scene will ultimately come together from the outset.
LINKS:

Jason Ryan demonstrates drag and overlap in this great video tutorial.

Yours truely with some thoughts and observations on drag.

Keith Lango on the zen of lead and follow in Maya

Keith Lango on using breakdowns to create overlap.

Cameron Fielding shows his simple techneque for animation overlap in Maya.

Mark Kennedy from the Temple of the Seven Golden Camels blog shares some notes on Follow Thru.

Another great one from Kieth about choosing the right time to offset keys.