Skill based

A skill based system is a method of mechanically representing entities in an RPG as a collection of abilities ("skills") rather than membership to exclusive categories or classes.

In a skill-based system, rather than defining a person by the "level" they are in a class ("5th level wizard"), the character's abilities are governed by their points or ranks in given skills ("5 ranks in thaumaturgy, 3 ranks in elementalism, 0 ranks in necromancy"). Skill-based systems usually have as their improvement mechanic a means to earn and spend points to improve a specific skill, or to acquire new ; contrast this to class-based systems where points are spent to improve one's rank in a class or career, which improves a suite of abilities and only those abilities.

More complex skill-based systems will divide abilities into inherent attributes (usually sub-divided into physical and mental attributes), used in conjunction with acquired skills to determine a character's proficiency and chance of success at a specific task. These attributes will be applicable to many tasks, whereas acquired skills are more specific in use. It is normally possible for these attributes to be improved by the expenditure of experience in the same way as skills, although at a higher cost because they are applicable to more uses. Simple systems, such as the clichés in Risus, will only use one type of skill applicable to many situations, to keep the list of skills (and thus character descriptions) shorter.

Games that have "skills" with ratings as part of character descriptions are not necessarily skill-based RPGs. The Warhammer system (WH Fantasy, Dark Heresy) has careers, but each limit the skills you can acquire, and you must acquire these skills before you can advance to another career. The systems used by Dungeons & Dragons have their non-weapon proficiencies, or skills in later editions, but improvement of the character is inexorably tied to advancing in the characters "class" which determines how you can improve skills and restricts allowed skills.

Consider Dungeons and Dragons, where in 4E a character's competency in the application of any given skill is not only based on their attribute and whether they possess training in that skill (a one-time flat +5 bonus), but also their class level. Furthermore, their class determines what they are allowed to be "trained" in, and improving class level is the only means for improving skill success (which improves all skills simultaneously). In contrast, in a skill-based system such as World of Darkness, a character who wishes to become better at a specific skill can at any time spend the experience necessary to improve a skill and only that skill, usually at less cost, allowing for true specialisation.

All the cool kids are playing skill-based RPGs.

Benefits

Skill-based systems are generally considered to produce more realistic individuals than level-based systems, since achieving a high degree of proficiency in a given skill does not also necessitate improvement in many other, potentially unrelated areas.

Advancement in skill-based systems is faster, because the points spent don't have to be wasted on class or career features that the player will never use.

• tl;dr: You can become a surgeon without accidentally being a champion race-car driver at the same time. You don't have to wait until you're 70 years old to become a surgeon.

Drawbacks

Skill-based systems can get bogged-down in bookkeeping, as designers add more and more specific skills to increase the accuracy of simulating scenarios (q.f.: GURPS). This gets compounded when some skills have "prerequisites" of a high enough rank in another skill. This can inflate the number of sourcebooks needed for a well-rounded character -- which book publishers enjoy, but gamers don't wish to carry a library to each gaming session.

For skills or attributes that have a more general use, game-balance can be difficult to maintain. For skills that have a more specific use, it's implied that people who don't spend points to acquire that skill are incompetent. For this reason, many systems give starting characters a 100% rating in "Speak: English" just so they can have 0% in all other languages. A well-known example is how few players put points into the skill "swimming".

• tl;dr TOO BAD YOU ARE ALREADY DEAD.

Notable Examples

• GURPS - the ur-example, players are described only by four attributes, inherent 'merits' and 'flaw', and a plethora of skills.
• Risus - characters are defined entirely by "Clichés", such as "Viking", "Wizard", or "Bumbling Hero", with a numerical indication of their competency (or incompetency) at tasks that would fall under the purview of that cliché. You would use the cliché rank to determine success chance for any task the players can agree would be familiar to stereotypical "Bumbling Viking Wizard."
• Traveller - although character generation is class-ish, with the terms served during one's career, the resulting character is only attributes and skills, and character improvement is improving skills or acquring new ones.
• World of Darkness - uses a 0-5 "dots" representation of attributes and skills, divided into broad categories of physical/mental/social/supernatural (the latter being vampire disciplines, garou gifts, mage spheres, etc)