"Fit" in psychology training tends to be a mix of the program culture, match between mentor and mentees, and a more practical consideration of skills needed.
1. Culture: This is part to do with model (scientist practitioner, practitioner-scholar, etc.) and part to do with the more general culture of the program and area.
2. Mentor/Mentee Match: It isn't so much that the mentor and mentee have to have the same personality (sometimes that is a volatile combination), it is more about having the mentee match up in regard to training style and culture of the research group. Some labs benefit from having a mix of personalities, while others will grind down a person who doesn't fit.
3. Practical skills: Some labs need someone who has more of a programming background, others need someone who has a particular strength in X topic area. Often this preference isn't really known to the applicant and sometimes it isn't something that is explicitly sought by a mentor, but it can pop up when considering contrasting backgrounds of applicants.