You basically have 6 major roles in league:
- ADC - Deals lots of physical damage, relies on Auto Attacks, piques mid-late game.
2)APC - Deals lots of Magic Damage, relies on Spells, piques mid game, can carry into late game.
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Tanks - Lots of HP, Magic Resist, and Armour, they usually have 1 or 2 reliable forms for Crowd Control, their job is to be in the middle of the enemy team and disrupt them.
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Assassins (can be AP or AD) - Their job is to do lots of damage, near instantly, to quickly kill a target, usually an APC, ADC or Support. They also try to pique as early as possible, and tend to do well early game, and mid game. If they fall behind though, they tend to be a liability more so than an aid to the team.
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Support - They have general utility weather its healing, shielding, buffing, or utilizing Crowd Control. Its their job to help the team out by being able to give more vision, and being able to build items that benefit the whole team, as well as them selves. Disclaimer Its everyone's job to ward, but supports get the flack if there aren't any.
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Bruisers (can be AP or AD) - They are a hybrid between either an Assassin or APC/ADC and a Tank. They get pretty beefy, but can deal some pretty good damage.
As for the lanes in League at the moment you have.
Bot Lane - Usually has a Ranged ADC + Support/Tank. The ADC Tries to farm minions while the Support/Tank protects them.
Mid Lane - Usually has a solo APC/AP or AD Assassin/AP Bruiser. Its basically a duel vs you and the other teams main source of AP damage.
Top Lane - Usually has Melee ADC/AD Bruiser. Essentially the same as Mid lane, but with AD Champions.
Jungle - Can contain virtually any role. Jungle is the hard one to pin down for specifics mostly because literally any type of champion can be a jungler, and each one fulfills the role differently. It widely depends on the champions kit, some excel at assisting other lanes, others do really well stopping the enemy from getting their jungle monsters, which are the main source of gold and exp for a jungler. ( think of them like minions for junglers)
Hoped this helped some what.