Very rusty about all of this, but here goes. 'Psychometric tests' can cover a whole range of things. However, the tests are likely to mean either personality tests and / or aptitude (ability) tests. As previously mentioned the psychologist will be present because these tests should only be administered and interpreted by someone who has been thoroughly trained in their use, and more often than not this will be a psychologist.
Personality tests aim to explore different personal characteristics in a candidate, e.g. the degree to which someone is extroverted or introverted, whether someone likes to operate on their own or part of a team, whether they are impulsive or must think out problems carefully, whether or not they are trusting of others or naturally suspicious etc etc. All of which are measured on a scale. There are absolutely no right or wrong answers on these tests - everyone's personality is valid! Your friend shouldn't try to second guess what the organisation is looking for as she will be rumbled: There are 'faking good' scales built into them that try and assess the extent to which a candidate is trying to portray themselves in a good light.
If the company is using the personality tests responsibly the results will only ever be used in addition to other more important information about the candidate. They may well interview her and explore aspects of her personality that may appear to conflict with how they see the role, e.g if its a sales position and the person is very introverted then they may wish to explore with the candidate how they go about building up contacts and networks, or if the job requires a meticulous planner and the candidate's personality suggests that they are much more of a 'come up with ideas and walk away' person then they might probe about their planning skills or boredom threshold.
The other most common type of psychometric test is an aptitude test. They aim to measure people's abilities in a number of areas, usually verbal reasoning, numerical reasoning and abstract reasoning. They are not designed to test someone's knowledge (or education) at all - they try and tap into people's underlying abilities (which is why they are so attractive to employers). The company should have sent your friend a 'practice' or 'familiarisation' booklet explaining what the tests she will be sitting are about. This is good practice. She should phone up and ask for one (every published test has one). If your friend is particularly worried about the aptitude tests then she could always buy one of the books available (in most career sections of book shops) that claim to be able to improve scores on these tests. What these books CAN do is familiarise someone with the format and content of apitude tests thereby increasing confidence and reducing anxiety. However, they CAN'T significantly improve how someone will perform on them.
It is also worth bearing in mind that there is no 'pass mark' on aptitude tests. Your friend's results will be compared with how another group of people have performed (e.g. graduates, school leavers aged 16 or engineers) and she will be given an above average, average or below average rating. Again if the company is using the tests responsibly then the results will only be used alongside other information about the candidate - the psychologist will be there to see that this happens (its not in their interest to see these tests abused).
Hope that helps.
Good grief thats blown some cobwebs away!