What are they?
Essentially, psychometric tests are tools for measuring the mind ('metric' = measure; 'psycho' = mind). There are two types of psychometric tests:
Aptitude tests: which assess your abilities. Personality questionnaires: which help to build up a profile of how you may behave in work situations and how you prefer to work.
How are they used?
Don't panic, psychometric tests are used by employers in conjunction with more traditional selection methods, such as a one-to-one interview or an assessment centre. So if you don't do particularly well with the psychometric tests you've always the chance to impress at an interview.
Employers can use these tests at any point during the selection process. Sometimes they are used at the beginning, as a way of screening out unsuitable candidates. Other employers prefer to use them towards the end of a selection process.