An assassin is somebody who's career or task is one that involves the removal of one person or more from ability to carry out their actions as normal either through death or incapacitation.
An assassin is also a general term as this may for example, be somebody who is simply focused on the killing of one person while not necessarily being somebody who's career is based on the concept of killing for reason.
Often assassination is a clean killing action, avoiding making traces of evidence that they were there, or how the person died while using minimal effort if possible and making a minimal amount of mess through the killing. Assassin's methods will vary, sometimes depending on where they are situated for their mission or who they are attempting to kill.
For example, as brutal and dark as it may sound, somebody may be in a car or an armoured car. To get the target who is protected, it may be that the use of a car bomb is used or a bridge which the vehicle may pass over is destroyed. Or one may poison a drink, though people who suspect of assasination attempts on their life, will usually avoid drinking anything that could potentially have been swapped for or may have been poisoned.
The reason such people would take this career or choice against others is not necessarily money or material gain. A person who makes hits on people according to a statement or request by somebody is an assassin who may be called a hitman or contract killer. The contract is an agreement after the person has requested the death of somebody, that the assassin will carry out their mission.
Some assassins may do this for political reasons or reasons of faith or insecurity. How often this may happen always varies, as such in a modern society it may be harder to carry out a kill due to legal limitations such as the inplementation of laws or law enforcement.
Assassins vary in concept and code through fiction.
The word "Assassin" was originally used to refer to a specific group, the "Assassins" or "Hashashin", a Shia Islamic religious cult group from the Middle East (mostly based around Syria and Persia) that was responsible for many assassinations during the Middle Ages, from the 11th to 13th centuries, usually targetting the leaders of Sunni Islamic and Christian Crusader states.
One of the earliest assassins in video games is Sadler from the XZR / Exile series, an action RPG franchise that revolved around the original Assassins group of the Middle East. Very few games have since dealt with the original Assassins group until the release of Assassin's Creed, which revolves around an Assassin called Altair.
A much more common group of assassins in video games are Japan's' Ninja, though they are more often inaccurately depicted as powerful warriors (such as the Shinobi and Ninja Gaiden series) rather than assassins. One of the franchises that more accurately depicts Ninja as assassins is the Tenchu series.
An early video game example of a modern assassin, often referred to as a hitman or contract killer, was Golgo 13, the protagonist of the Golgo 13 series of manga, anime and games. Assassins are also a common occurence in the Metal Gear series of stealth games.
Agent 47 from the Hitman game series is a modern-day assassin who in canon, uses discreet methods by making the most of the intelligence he has on his target and surrounding areas. He would have a greater array of weapons than say, somebody such as Altair or Ezio from the Assassin's Creed series. Some assassins may choose to fight differently and have less at their disposal than Agent 47 or Altair and Ezio; assassins such as Thane Krios from Mass Effect 2 chooses to snipe his targets from afar where he will not be noticed, defending himself with a sub machine gun and systematically eliminating threats in close combat if possible.
Assassin as a concept is also used in class; while there is not specifically a dominant story or an exact set of skills to be chosen in The Elder Scrolls, the concept of an assassin does remain, but there is more choice how a player may go about this skill-wise and the story for their character is their own.