The number of charges determines how many times an item can be used. When all charges are spent, the item will dissappear.
For runes, you must actively "use" the charges, but for Amulets, Necklaces and Rings the charges are automatically used as needed (while the item is worn). For example, if you are wearing a Silver Amulet, then a charge will automatically be used every time your character receives Poison damage. On the other hand, a Heavy Magic Missile rune will not lose charges unless you "use" it to attack a creature or player.
With the 7.8 summer update, the number of rune charges left appear on the rune itself, so it is no longer needed to "look" (SHIFT + Click/ Double click) on all runes when trading with others to see the runecharges.
With Summer Update 2010, runes no longer have charges but have been replaced by stacks. An old rune of 4 charges are now a stack of 4 runes which now weigh 2.10oz.