In the Destruction skill, I now have sufficient points to choose the Rune Master perk. Its description says that I "will be able to place runes five times farther away" but I haven't the slightest idea what a rune is or what this means. Can someone shed some light on this?

A Rune is a Magical Trap Spell, that can be cast in an area an Opponent needs to cross. The Spell activates when an Enemy gets close to it. Rune Master makes casting Runes far away easier, but a Rune Spell can not be used to make a Minefield, just individual Mines

It is a useful Perk for a Sneak Mage casting silently.

Runes are basically magical traps, it's a spell-in-waiting cast on a surface that only activates when someone gets close enough to set it off (and take whatever damage it inflicts). They come in the same three elemental flavors as your other destruction spells and so do Fire, Frost, or Shock damage depending on which type of rune you cast.

More info here:

http://www.uesp.net/wiki/Skyrim:Fire_Rune

http://www.uesp.net/wiki/Skyrim:Frost_Rune

http://www.uesp.net/wiki/Skyrim:Lightning_Rune

There is a distance at which you can cast a rune, if the surface you're trying to cast it on is too far away you will not be able to place it there without getting closer. The Rune Master increases the distance at which you can successfully cast a rune. Runes can be very handy if you are a sneaky mage who would enjoy laying traps for enemies and then luring them out to set them off and take damage from them. Being able to cast them from much further away only increases their usefulness since you would not need to get as close to potential enemies in order to cast a rune in their path.

runes are destruction spells that are cast on the floor. once an NPC steps on it it will explode.