Backdooring typically refers to the act of taking out an enemies base tower or inhibitor/barracks while the enemy team is slow to respond to your presence, unaware of your advances on their base (due to poor map vision coverage), or otherwise occupied with fighting or pushing on their own.
Generally speaking, in League of Legends, a backdoor will occur while one team is pushing on 5v4, while the last remaining member of the defending team goes to take out towers. Strong backdoor champions include Master Yi (due to his high autoattack damage, steroid skills, and high mobility), Twisted Fate (long range ultimate), Pantheon (long range ultimate), or any other character that excels in dealing auto-attack damage and pushing.
Backdooring is not explicitly disallowed, nor is it a core part of gameplay (meaning you wont see a backdoor happen every game). However, as a rule of thumb, it's generally looked down upon by people in mid to low ELO brackets. You generally wont see it happen as much in higher level play as the enemy will be much more attentive of problem characters like that and wont give them the chance to do so. It's a perfectly legitimate tactic, just difficult to pull off in higher levels of play.
It should be noted that you should not be confusing "backdooring" with "split pushing". Split pushing is when the offensive team attempts to take down two or more towers simultaneously through the use of a single lane distraction. For example, a team may send 3 players to a single lane to push on the tower. The defending team overcompensates and sends all 5 to defend said tower and hopefully secure a few kills. Meanwhile, the other 2 offensive players have full potential to go and destroy another lane's tower.
In both cases, you can utilize long range ultimate characters like Pantheon, Twisted Fate, Nocturne, Shen or Karthus to dissuade or completely stop split pushing / backdooring. Additionally, the summoner spells Teleport and Fortify are great for preventing these tactics. It's not uncommon to have at least one person running Teleport on a team, and in Draft matches (where you have the ability to see the enemy team during champion select), it's often wise to have one character take Fortify if you identify their team as a push team.
Best Answer
I believe you are referring to the Parallax Scrolling technique.
Referring back to the screenshots in OP, this appears to be the technique in play. In order to create the 3D depth illusion a number of images are layered, with the bottom most images on top. Each layer will scroll at a different speed.
To simply the scenario, consider the game screen is split into 3 images:
The foreground is layered on top of the ground, and the ground is layered on top of the background. The background will scroll slower than the ground. The ground will scroll slower than the foreground.
Consider the screenshot in the bottom right.
The grass is in the foreground, and will move across the screen much faster than the dirt pathway as you walk left/right. Also, it will appear over the road and any characters in this plane. The mountains will scroll much slower in comparison to the dirt pathway. Additionally, anything in the plane of the dirt pathway such as characters will appear over the background.
I have used an example of 3 planes, but you will probably find the background has multiple planes itself (e.g. the clouds may move slower than the mountains). The main ground will also have its own plane system so that items lower down the axis will overlap items higher up. To complicate matters slightly, this is different from a character jumping (they will move higher up the screen but remain in the same axis/plane).
As mentioned in the comments, this technique is part of the 2.5D technique.
The Parallax Scrolling technique is used in a large number of games. Streets of Rage and Street Fighter spring to mind. It is also implemented into the SCUMM game engine (although this game engine additionally offers sprite scaling on the y-axis).