Why is it that certain champions do better in certain lanes than others?

It's all based on the geography of the map.

Bot lane is the duo lane because of the additional dragon control. Lane swaps do happen, but they are typically based around getting the ADC fed as fast as possible, or it's used to get an early tower before a dragon attempt can be made by the enemy team.

Mid typically has burst champs with high mobility or CC, due to their potential for getting easy kills from roaming around the map. With mid lane being literally at the center of the map this makes mid the single best lane for roaming.

Top lane, since it is near no early game objectives, is the island, and has champions who do well on their own. Top laners can roam, but they typically push down their opponent's tower before either continuing their push, drawing additional opponents to stop them and thereby lowering pressure on the rest of the team, or by roaming to use their advantage to get objectives faster than the enemy team.

Jungle is pretty self explanatory. If you can survive the jungle and have either the CC or damage to make the enemy team worry about ganks you're fine.

Now, matchups are a large part of this answer as well, but the geography decides where these matchups take place for the reasons stated above. Some champions don't need the geographic advantages, or can get around the disadvantages, but simply do better against champions who are drawn to each lane based on it's geography.

Matchups or The length of lane allows them to do more damage because they can chase longer or Rengar/Kha Zix bush passives or Ease to gank/be ganked or Roam availability or Counterjungling

Here are additional factors to consider about why certain champions are better off in certain lanes.

Damage: What type of damage does your champion deal, and how much? Aggression: Is your champion a lane bully? Sustain: Can your champion heal or shield him/herself? Type of Resource: Does your champion use mana or non-mana? Mana costs: Is your mana champion mana hungry or is mana barely an issue? Mobility: Is your champion mobile or immobile? Cooldowns: How long are the ability cooldowns of your champion? Utility/Crowd Control: Is there any crowd control abilities in your champion's kit? Durability: Is your champion squishy or tanky or in between?

Extra Credits explained this pretty well.

In a nutshell: Top lane is a wild card because it is so isolated from the rest of the game, and that there has been several meta-shifts, but usually they either have the durability to survive the extended fights or mobility/kiting to reach tower with safety. Mid lane has bursty champions so that they can kill each other before one ends up running to turret. These champions are usually squishy, and appreciate the short lane because they don't need a lot of mobility or durability. Bot lane has the damage dealer, but they aren't safe until they have scaled, so with another champion that can support them through their weak phase, they will emerge a threat later on. They also are "conveniently" placed next to an early game objective. Jungle has a number of benefits and safety due to stealth, so this is usually where those that cannot survive in a lane end up being placed, and are expected to create map and objective pressure with their large roaming territory.