When you're designing a 3D model for print or video there's little need to pay any attention to reality. Most scenes and objects will only contain the meshes that are visible, objects don't need to really connect, etc. You can completely ignore the physical world.
As some of you have already discovered, once you start working with 3D printers this is very different! This mini-tutorial will cover a few common pitfalls that I encountered over the last few weeks.

3D printing companies like to call this being 'watertight'. It can sometimes be a pain to identify where this problem occurs in your model. If you can't find it, try AccuTrans - it will highlight the problem area for you.

The full definition of manifold is quite mathematic. For our purposes, a mesh will become non-manifold if it has edges that are shared between more than two faces. Here's an example:



The two cubes in this example have one edge in common, so this edge is shared by four faces.
Blender has a feature which will help you identify non-manifold areas - let's try it out on our non-manifold cubes:



And presto:



I'm not familiar with how other tools handle this. Please let me know and I'll add the information here.

All surfaces of your model should have their normals pointing in the correct direction. When your model contains inverted normals our printers cannot determine the inside or outside of your mesh or model.

While modeling for 3D Printing is quite different from 'traditional', it isn't hard - if you keep the constraints in mind from the start.
I hope this tutorial gave you a good jump-start!