So the main idea is efficient use of resources. There's only a limited number of lane minions to provide gold and xp to your team. Without a jungler you split 3 Lanes among 5 players, with a jungler you split it across 4 players, and your 5th player is just as strong as your first two.
A late game level-line (when no one is getting kill xp) may be something like:
Top and mid: level 16
Jungler: level 15
Adc: level 14
Support: level 12/13
Without a jungler that would be:
Mid: 16
Adc/one top: 14
Support/second top: 12/13
That's like 4-5 levels of advantage ignoring all kills and the extra gold.
Now as to the other reasons:
Smite is useful all game in the jungle, but relatively useless for a laner. Yet it's an important summoner spell for securing dragon and Baron (getting the last hit to get the buff for your team, rather than the enemy stealing it). Objective control is very important and is the junglers job. A team that's clear in the lead can lose the whole game by letting Baron get stolen.
Early game you can handle a 1v2 Lane. It SUCKS i agree. However the tower is strong so you're relatively safe there early on. You'll level up faster so it's not as bad as a 1v1 Lane where you're equal and then he randomly gets an ally that's also just as strong. Experienced players are willing to sacrifice the feeling of winning themselves so that the team can win.
The most important reason is to have a player "hidden" or missing on the map. It forces caution on the other team. You can't go too aggressive on your Lane opponents because the enemy jungler could be hiding in a Bush nearby ready to turn the 1v1 or 2v2 in to a 2v1 or 3v2 and beat you. So even if your allied bot Lane is worse than the enemy, the enemy may be unable to get anything out of it because they're afraid of your jungler tipping the scales in your favor. When they do eventually make a risky play to try to get a kill, the jungler being there can turn 2 kills for the enemy team in to 2 kills for your team.
Of course, in completely new play most of this is entirely unnecessary. Players struggle enough 1v1 let alone 1v2. Junglers don't know how to pick when and where to gank, and probably let the other team see them just running into a Lane to pick up a creep or two as they play. Skill levels are likely so different that a jungler may not make a difference in that 2v2 / he'll be needed in more than one spot at a time. Finally, you lack runes and masteries that add lots of stats early game to help a jungler stay healthy while he does jungle camps - preventing him from getting sufficient gold and xp early in the jungle and causing him to steadily fall farther behind. Thus double top can work a lot better for most new players. Eventually it will be clear that having a jungler is really important though. I'd suggest watching a few higher level games if you're really interested.