Like in real life and any other video game, the goal of an Assassin in League of Legends is to quickly kill high priority targets. An assassin’s strengths lie in their high mobility, often having one or more methods of getting deep in to or out of a fight, and in their high burst damage, which allows them to efficiently remove enemy threats. Assassins are susceptible to focus-fire and crowd-control, as they lack the innate tankiness to survive such damage and effects.
An example of a strong single-target assassin is Zed, the Master of Shadows. He is a physical-damage focused assassin that specializes in jumping to an enemy carry, killing him, and escaping back to his original position. Zed, like many assassins, has a high skill cap, meaning he is very difficult to master. While Zed has methods of escaping enemy focus, his escape mechanisms are typically used offensively to increase his damage. Once these skills are on cool-down, he is an easy target to eliminate.
Another example of an assassin is LeBlanc, the Deceiver. She is a magic-damage focused assassin that specializes in mobility, burst damage, and deception. With her ability to manipulate a clone of herself, she can dash into an enemy, kill them, and escape by tricking the enemy into confusing her and her clone. LeBlanc underwent a rework that caused her damage to be over a slightly longer period of time, but she definitely does not lack damage.
Because assassins lack durability and rely on killing enemies to be effective, outlasting an assassin in a fight by building defensively is a great way to deal with them. Assassins are typically a lot of fun, but very difficult to play.
If you think dashing around the map and killing enemy carries in the blink of an eye sounds fun, assassin might be the role for you!
To learn more about another role, check out this guide on mages!