Your version of relaxing definitely sounds  more "Relaxing"... What relaxing a UV map does is akin to smoothing out and flattening a wrinkled sheet over a bed I guess. it eliminates or minimizes distortions in the map by attempting to equalize the edge layout of the map. It helps to eliminate bunched up polys that you often see at the edges of map regions, These bunched up polys in the map make a mess of your texturing attempts and often make glaring seams in your textures (or so I've found).

Here's a really tech explaination... http://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm

You might be well served by these Hex tutorials, they look pretty good...

http://www.geekatplay.com/hexagontutorials/

Can't really offer too much specific advice about Hex, as it's not my weapon of choice (I have the latest version but it's incredibly unstable on my computer).

cheers