What are they?
Edgeloops are Loops of Edges that either end where they begin or end at an edge of the geometry. They Don’t end at a Pole (a Y with two or more loops split from the end of the original loop) and they are not RingLoops (circular loops that run around a cylindrical shape).
Edgeloops define the base shape of an object and all other geometry defines the detail between them.
Edgeloops are important (to understand and to get right) because, as it is them that define the integral shape of the object, and because they extend (uninterrupted) into all parts of the object (from the thumb up the arm over the shoulders down the other arm around the thumb back up below the elbow and around the chest down below the first arm and back to the thumb) they have to work right in order to keep the details between them from pinching, stretching or otherwise distorting when animated. Even in stills you’ll get bad texturing/lighting artifacts with messed up geometry; ie, bad edgeloops. They are the foundation for everything that is cut into them afterwards and all the Materials, Textures and Normals for lighting.
http://www.suchyworks.com/tutorial/polyvantage.html
Check out page 3 and beyond
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What Fligh says is true, but the term is also used slightly differently in Blender. Edge loops in Blender are basically whatever you can select by clicking Alt-RMB on an edge. If you select something with Alt-RMB, and press the X key to delete, and choose “Edge loop”, the verts you’ve selected will be removed but the mesh will stay intact. These “edge loops” are not alway strictly true edge loops in the sense that Fligh describes. Both ring loops and edges that end in poles can be selected with Alt-RMB and deleted with X>Edge Loop.