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There are so many fail statements about tier lists on this forums.
Q: What is a tier list?
A: It is a list of champions sorted by power.
Q:What does _power_ mean?
A: Power of champion is ability of a champion to do his job. For example Jax is a stronger melee character than yi.
Q:But I did well with yi while jax fed?
A: Each champion performance is a sum of three things: skill + team composition + power of champions. Skill > team composition >> power of champions. So you just played better.
Q:What for do you need tier lists if power is small part of the game?
A: If you are playing at tournaments you need all advantage you could get. So you will want to get the best tank, the best dps and not good tank and good dps. Also you could try top tier's champions if you are not so good in this game, this will get you advantage, but remember skill + team >> individual champ power.
Q:I see a lot of angry posts in tier list's threads.
A:Many people hate than their eve is called UP champion. They can't understand that this doesn't mean that she is auto lose.
Q:What tier list is the best?
A:There is no such list. Power is very hard to calculate and you have 50 champs you need to put in right place (50! options), also they are metagame dependend. The most lists you could find on this forums are good enough to use.