Character Class is an RPG mechanic that defines a PC's skill set in terms of a specific, defined group of abilities - often derived from a hypothetical occupation1.
Most RPGs at least attempt to balance skill sets between classes - mileage may vary in all cases and it is quite common for any RPG system to have a known gradient of classes (usually based on their killing power), especially taking into account development and progression of powers within the various classes.
Arguably the main advantage of a class system is that it allows inexperienced players in particular to have a "walk up" character concept which comes with all the skills that it needs to fulfil a given niche in a group and doesn't omit key skills which might otherwise be forgotten and leave a glaring gap in the character's repertoire.
The "hardest" class based systems (such as early editions of (A)D&D) make it very hard for a character to progress in more than one class - or otherwise develop skills from outside their set. This has the advantage of allowing the designers to preserve class skill niches and class vs. class balance for much longer (only the cleric heals, only the theif can climb walls, pick locks etc.), but can lead to ridculous incongruities including it being literally impossible (within the rules as written) for someone to attempt something outside their skillset (fighter cannot climb tree - only the theif has the climbing skill) and no-one having any skills that aren't directly related to their class's ability to kill things. These incongruities are usually softened by "cross class skills", background skills and the ability to pursue multiple classes - although such things took a long time to develop historically - but only at the cost of added complication2.
At its softest "classes" may appear in what are effectively skill based systems, purely as a descriptive template3. Even a fully skill based system may include class like "kits" or "lenses" that serve as a guide to building specific character concepts.
In general, the harder the class system, the more gamist the style of play to be expected - a less gamist approach undermines many of the advantages of class differentiation.
Where character progression is measured in discreet levels of power, this feature can be part of a class and level system.
Game and Story Use
- The idea of tiered character classes can be very easily scrambled by running a campaign where killing power is less of an issue. A "top tier" class rated for killing things in dungeons is highly likely to be a liability in a politics based urban campaign.
- Best to make sure that your players know what sort of campaign you are planning in advance - players who want to play slaughter-hobos will not be happy in a roleplay based campaign, whilst others will still want to take the theme of the campaign into account in their choice of class.
- Realistically, character class can be a marmite mechanic - and if you don't like it, you may be better off playing a system that runs on a no-class or soft-class basis.