Personality testing is big with many companies. Employers are using instruments like the Myers-Briggs Type Indicator and Big Five personality tests for things like assigning employees to teams. Some companies use them in hiring decisions, and that can be a problem.
The creators of the MBTI specifically state that the test shouldn't be used for selection. They specifically state that no personality type is better than another. The test is a self report measure of one's personal preferences for interacting with others. It doesn't claim to measure ability or motivation. Some researchers question its validity and reliability, and the evidence that it predicts on-the-job performance is mixed at best. But the tool is out there, and HR types are going to use what tools are available when they need help with selection.
Disclaimer: Even though I'm a Ph.D. psychologist, I didn't study personality theory in grad school. I haven't read the primary literature, only the HR and Org Behavior textbook versions of the literature, so I don't claim in-depth knowledge about personality testing. Apparently, though, there is evidence that the five-factor model (Big Five) predicts job performance for certain kinds of jobs. Researchers point to some studies that show that people with high scores on the extroversion and conscientiousness scales tend to perform well on the job. Those sorts of results are enough to encourage HR departments to employ the tests for selection.
What does this mean to you? If you're presented with a personality test during the hiring process you would be advised to answer in a way that maximizes your extroversion and conscientiousness scores. "I love to go to parties and talk to a lot of people. Agree or Disagree?" "I'm not satisfied until the job is done. Agree or Disagree?" The questions are nearly that obvious. What you want to do is get past the HR screening portion of the selection process and talk to the hiring manager about the real requirements for the job. At that point you can find out whether things like mixing with strangers at parties is a necessary function of the job.
Good luck, and let me know if you encounter personality testing during your interview.