What do the names mean [duplicate]

These are the current Champion roles and their descriptions as the client describes them (note that roles only suggest how a champion should be played like, and not restrictions):

• Assassin: An assassin is a champion who specializes in seeking out weak targets, killing them quickly and mercilessly. Because assassins focus upon infiltration, deception and high damage abilities, they are often less durable. Assassins are solitary hunters who bring instant death to the weak. (Tl;Dr Semi-burst, melee, anti-squishy role that sacrifices tankiness for killing power and mobility)
• Fighter: Fighters are durable melee combatants that focus on a mix of offense and defense. While they don't wield as much utility as a tank or as much kill potential as an assassin, the damage from a fighter adds up and becomes a major threat over time. (Tl;Dr Also known as Offtanks and Bruisers, a melee class that is able to deal damage and survive in the middle of a teamfight. They tend to have some form of CC and chasing ability.)
• Mage: Mages inflict burst of ability damage at range, but sacrifice defense to do so. Bringing high damage potential and utility, mages can lock down entire areas, quickly destroy a valuable target, or capitalize on clustered foes to decimate the opposing team. (Tl;Dr Some mages are squishy and bursty (long cooldowns, high damage, ability synergy), while some are tankier and have a more constant form of damage (short cooldowns, meh range). Mages always have CC and AOE abilities, and always deal magic damage)
• Marksman: A marksman is a ranged attacker who deals continuous damage to individual targets, but sacrifices defensive power and utility to do so. Typically focused on using basic attacks more than abilities, marksmen scale their damage output to devastating levels in the late phase of the game. (Tl;Dr AD Carry, heavily item reliant, uses AutoAttacks and deals insane crits. Very easy to kill as their build consists of items that either look like one sword, two swords or three swords (maybe some other type of weapon in rare cases, but mostly swords))
• Support: Supports defer some power to augment the power of their allies. They often assist their teammates by healing an ally or increasing the ally's damage, but can also create combat opportunities for a team through strong crowd control abilities. A skilled support can give a team the edge it needs to claim victory. (Tl;Dr Barely any damage or in some cases tankiness, but they don't need items, so they keep their carries safe while those farm. Nearly every ability a support has is either a buff or a form of crowd control)
• Tank While they don't deal the most damage (say that to Malphite...), tanks are durable, front-line champions that lock down enemies and start fights. They usually lead the charge, choosing the right moment to initiate aggression. Many tanks can also protect squishier teammates by immobilizing dangerous foes and limiting their ability to inflict damage. (Tl;Dr Their job is to initiate and make sure everyone attacks them to give your own team the opportunity to do their own tasks in the fight. Tanks have an initiation ability (usually hard AOE CC ultimate), and a kit to make them look menacing and not be ignored. They have utility, but can be outmatched in every aspect except for one, and that's surviving a burst from 5 people)

I suspect you're asking about the champion roles listed by Riot in the PVP client and on the website (seen here).

If so, Those are roles for each champion.

• Assassin - Aims at killing 'squishy' (low maximum health) targets quickly.
• Fighter - Generally a mix of both a damage-dealer and tank. Can take a hit and can dish one out.
• Mage - Generally spell reliant, casts many spells. (Typically AP based).
• Support - These champions are generally seen as those who focus on helping another champion instead of farming or laning solo. They typically have heals, buffs and debuffs, or crowd-control.
• Tank - Most durable of champions. High health (usually) with high resistances compared to other champions. Typically has some way of either disabling enemies, making enemies focus them, or both.
• Marksman - Shoots from afar. Always ranged. Typically this is your AD carry.