I played a lot of ranked, almost 1600 elo atm so I'll try to answer. In order of importance, here is what I think goes into the picks:
1.Role
Each person on your team should have a role. You don't want to pick multiple champions that can only jungle or only mid/top. Unless you've agreed with your team pregame, usually you have 2 bottom, 1 jungle, 1 mid, 1 top. Pick champions for available roles.
2.Counterpicking
In a lot of organized teams and high elo games, people usually pick ad carries or support champions first, since these are generally hard to counter because of the role they play. The ad farms and the support provides utility, roles that's difficult to counter. Mind you, there are specifics like sivir being good against Caitlin.
For the rest of your lanes, you have to be very careful about counterpicking. This is why it is always a bad idea to first pick kassadin, as he has numerous counters that simply prevent him from laning at all.
A lot of people also pick champions that can fill multiple roles to throw people off. For example, when I pick gangplank, he can go top or jungle. If my opponents pick pantheon, gp's hard counter, I go jungle and have a teammate pick another top.
3.Team composition
You have to pay attention to how your team can work together and work to win team fights. Picking for roles and counters do little if your team doesnt work. I'll list the most common team comps:
A. Poke team
Your team has the ability to do significant damage from a distance over time. This allows you to slowly push down towers or seize objectives.
B. Standard team with moderate CC
Basically you have some crowd control abilities that allow you to protect your carries and shut down the enemy team.
C. Gank team
Your team has a lot of mobility and always maintains map presence. Good examples of gank teams include heavy ganking junglers like alistar or champions that can pressure globally like shen, karthus, or twisted fate.
There are many more, experiment!
An "Elo Rating" is a method games, usually Online Multiplayer games, use to separate stronger players from players who aren't as fortunate at the game. Using this method, League of Legends chooses who you will play with when you play the Ranked games with other players. To establish an elo rating, you need to play a few ranked game and after a while, you'll be able to see your rating in your profile and while waiting in some lobbies. League of Legends starts new player off at 1200 Elo. Winning, especially against high-Elo opponents, will increase your own Elo rating. Losing will make it drop. The best League of Legends players approach or surpass the 2000 Elo mark.
Best Answer
1100-1400 ELO is a point where players aren't too familiar with the more difficult concepts of the game yet.
If Amumu isn't banned, who is going to kill him? In a coordinated and balanced teamfight, it's highly unlikely anyone but the ranged AD is able to effectively stop him. (Tanks are usually banned because they are harder to kill.) Many players may not know how to position themselves, or to stay alive so these hard to kill champions may be considered overpowered at this ELO.
Who wants to chase Singed through a mile of poison gas? Who wants to be hit into the air by a scary piece of rock? A lack of competency is most likely present at this ELO so therefore certain champions are able to take advantage of this and contribute more to the team.
At professional levels, more strategy definitely occurs during champion selection, but at this specific ELO which most of LoL's ranked players are in, these bans occur often due to the reasons above.