Okay so there are two parts to the meta:
1-1-2-J
and
Tank<DPS<Burst<Tank
The first part is to maximize gold efficiency. Naturally, there being 3 lanes with 3 individual streams of minions (and therefore exp+gold), you want to get at least one laner on each lane. If you have a Jungler, you are now taking advantage of a 4th stream of gold, the Jungle. This unfortunately leaves one champion starved of at least gold, so we tend to have one last champion who's really good at supporting the team even when on a lack of budget (which, somewhat obviously, is our Support). So, we have 1 guy top, 1 guy mid, 1 ADC bot, 1 support to protect the ADC bot, and a Jungler. As to why the duo lane goes bot, notice the Shyvana looking creature near bot lane.
The second part is role diversity. In some way, you always want at least one DPS carry on your team (usually the ADC), at least one Burst carry on your team (usually the mid laner), and at least one team fight orientated tank (Top, Jungle, and/or Support). DPS carries scale best on gold and don't care as much about levels, so it's perfectly safe for them to lane with someone leeching their EXP so long as they get the gold. This is where we get the traditional ADC+Support Bot lane. Burst Carries tend to scale really well on levels so a solo lane is preferable, but they are just as prone to death as an ADC, so we tend to put them in mid lane as it provides them the most protection (mid lane is the shortest lane, and therefore easiest to reach tower with). Tanks, finally, tend to be much more flexible and diverse than their damage carry counterparts, and are usually well adapted to defending themselves for extended periods of time (Top), constantly fighting and setting up ganks (Jungle), or operating with a limited gold budget (support). A balanced team will almost always want at least one member in every asset of this balance triangle, as it will prepare them for whatever the enemy team throws at them if played correctly.