So, there are a few reasons to stand behind a mob, the first three being generally useful to all melee, and the fourth being important specifically to Rogues (and Feral Druids, but they're just wannabe Rogues anyway.)
When you stand behind your target, you do more damage.
Standing behind a melee target negates that enemies chance to parry and block your attacks. In PVP, it negates their chance to dodge as well, but NPC creatures can dodge attacks from behind. Parried attacks do no damage, and Blocked attacks both do less damage, and are unable to crit. If you want to do the most damage possible, stand behind your target.
When you stand behind your target, you take less damage.
This rule is a bit less hard and fast than rule one, but a great many (heck, I'd go so far as to say most) PVE mobs in dungeons and raids feature one or more of the following abilities: Cleave, Breath, Shockwave, etc. The thing they all have in common is that they are targeted in a cone in front of their caster. That means, by standing behind your target, you are safe from these effects. While there are some encounters in which this logic is inverted, or where special mechanics demand that you stand in range of these effects, those are exceptions that you'll learn about on a case by case basis. For the most part, the area in front of a boss is analogous to what most PVE players refer to as The Fire. Don't stand in it. In PvP, players are, for the most part, completely unable to attack you if you are out of their line of sight - read: behind them. If you want to take the least damage possible, stay behind your target
When you stand behind your target, your tank takes less damage.
In general, when an NPC successfully parries an attack, their swing timer (the time before their next attack) is reduced by somewhere in the ballpark of .5 seconds. As a Rogue, if you stand in front of a boss, your attacks will be parried a lot. This will have the effect of making the boss swing substantially faster, causing the nice person who is tanking this boss for you to take substantially more damage. Often, this leads to a scenario referred to as a 'Parry Gib,' wherein a tank takes unhealable amounts of damage in a very short period of time because of a high frequency of parries. As a Rogue, you attack very very fast, and boss mobs have a high chance to parry. In PVE, If you want your tank to take the least damage possible, stay behind your target.
And finally, this last note is specific to Rogues:
When you stand behind your target, you gain access to additional abilities.
As a Rogue, you have three very important skills that can only be used if you are standing behind your target. Backstab, Ambush, and Garrote. In PVE, Subtlety Rogues use Backstab as their primary attack, and Ambush as often as possible (During Shadow Dance, whenever Vanish is available off CD, to open the fight). Assassination Rogues use Backstab instead of Mutilate whenever their target is below 35% Health. Combat Rogues do not use Backstab. In PVP, Subtlety Rogues use Backstab as a primary attack, and all rogues use Ambush to open with a large burst of damage, or Garrote to open with Damage over time and a Silence effect (particularly devastating against mages). If you want to use Backstab, Ambush, or Garrote, stand behind your target.
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The second level of action icons above the main action bar are all accessed with Ctrl + the function keys. Unless you remap them, of course ;)