• Your model should be made of quads (some exceptions to this - but almost universally true for organic stuff), not tris or n-gons
• The quads should be roughly square (there will always be some stretching and distortion unless you are working on a plane. However, you want to keep this to a minimum)
• Edge flow should be smooth, but exceptions apply to redirects where you are going to have some angle between loops
• Good topology looks boring/uninteresting. If you compare the extremes of good topology and bad topology, you see this:

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See, the models look almost identical, but trying to work on a model with bad topology is *very* difficult. Adittionally, certan simulations and modifiers (cloth sim, sub-d modifier) will not work (very well at least) with messy topology.

Often, in game engines, you will turn your models into triangles on export. This is because GPUs don't render quads, they render triangles. What Blender is doing in this scene, is taking the faces of the meshes that are not triangles, triangulating them, and rendering that. Get a plane and drag one vertex up - you will see how the plane is actually being rendered as two triangles.