The personality–job fit theory assumes that examining a person's personality will give insight into their adaptability in an organization. Basically, how well they will fit in and work. By matching the right personality with the right company you can achieve a better synergy and avoid pitfalls such as high turnover and low job satisfaction.
Person–environment fit: Says that employees seek organisations that are good match for them (the Organizational culture appeals to them). They also stay committed to these organisations if the fit is 'good'.
The organisational competencies are defined in order to look at the requirements of the company which an individual is applying to. The Individual is then assessed on these competencies and the competency fitment between the individual and the company is found out.
The competencies can be assessed using various tools like psychological tests, competency based interview, situational analysis, etc.
If the Individual is found out to be good on competencies defined for the company using the various tools, we can say that the Individual would be able to adjust in the company environment and work culture and would be able to perform at his Optimum level, taking the performance to maximum level when required.