As an example, let us consider the character Aragorn from the Lord of the Rings trilogy. A shallow approach could specify that Aragorn has a "favored enemy" in orcs (adopting the terminology from the D&D tabletop RPG system for class attributes), granting him a bonus to damage them in combat.
A similar approach would be to define that Aragorn "hates orcs", which makes him less prone to retreat from combat with them (this can again be implemented in the game mechanics).
In a system with more depth, we might define Aragorn as having a high level of "social responsibility". This can be hard to integrate in the game mechanics, but not impossible.
Furthermore, it points towards a different option for utilizing this personality element, namely in the creation of content to accommodate this personality element, and the direction of content towards characters. We might tailor a series of quests to Aragorn's player, providing a story-based response to the character personality.
This can be problematic in terms of development resource, so a different option is to "tag" the hundreds of quests generally integrated in CRPGs after the personality/integration elements of the character system, and direct them to the player content.
This is not as big a development resource issue as one might believe, since CRPGs generally have lots of different quests in order to accommodate different player preferences anyway. Note that this approach does not prevent any players from accessing any of the content, avoiding redundancy.
As an example, a quest involving helping a group of refugees would be in line with our Aragorn. What we need to do is make sure this quest comes to the attention of Aragorn's player. Even if this quest might have been available anyway, the fact that the content is directed provides a measure of responsiveness to the character generation choices of the player.
This kind of responsiveness to player characters is one way of providing a feel of agency. It can be further developed, even in a simple framework. For example, Aragorn might develop new personality elements over the course of play - either through the actions of the player, or by use of a point-buy system mechanic.
Integration of character elements: The different options for integration allow different advantages and correspondingly varied requirements on development resource. Three examples are suggested:
1) Rules-based system. As a fairly shallow example, consider that a player selecting the character element "arachnophobia" provides the character with a rules-based -2 to damage against all arachnids, and five character points to spend somewhere else. This form for integration mimics the GURPS system, and provides players a direct use of the personality system.
A point-buy based system furthermore has the advantage that it allows people to use it as much or as little as they like, or even ignore it, gaining no special benefits or advantages.
As designers, we obviously have a challenge of balancing such a system and provide due consequence to choices - a player may meet twice as many orcs as spiders, meaning that a spider phobia is worth less. However, game balancing is a regular challenge in design and these issues can be addressed.
In tabletop RPG rules systems such as GURPS, integration and personality components can be defined as advantages, disadvantages or neutrals, depending on whether they cost character points, or provide the player with character points to spend on advantages or stats, or does not alter the balance.
This is just one approach - other tabletop RPG systems have chosen to use die rolls to determine character histories (Mutant Chronicles) or combinations of selections and dice rolls (Traveller).
While not fully realized in either of these systems, one major advantage of tabletop RPG systems is that they permit a method for players to play the game mechanics better by utilizing their character elements. In this way, tabletop RPGs encourage both players who prefer strategic/mechanic challenges as well as personality/storytelling-based challenges to utilize their character elements.
2) Content-only system. A personality system could also mean that NPCs who give you quests related to arachnids try to reassure you they are not that dangerous (if the NPCs know, they might not realize until they have joined you in the dank and musty cave...)
This is an illustration of how the game can utilize the character personality information to modify or direct content. This would appear to be a powerful tool in providing a personalized experience - the player will realize their choice of character elements are being responded to.
Note that the character effects that the game system responds to can be anything - personality trait, background, a contact etc. (alignment, reputation and past actions in the game are already utilized to some degree in computer games). Content direction is one method of utilizing existing content in relation to complex character systems. Other options include e.g. ambience and environment reactions.
For both 1) and 2) above, a personality generation and response system gives the player an increased feeling of agency - a higher degree of impact from their choices when creating and playing their character.