The term "psychometric tests" covers numerical reasoning, verbal reasoning, spatial reasoning and psychological personality profiling tests. "Psychometric" means "the process of measuring mental capacities and processes" (Oxford English Dictionary). They are also called aptitude tests.
They're used by employers to provide an objective measure of your personal reasoning ability or an indication of your personality. You usually visit the employer to take the aptitude test under controlled conditions. However, it's becoming more common to sit them online before being offered an interview - especially with graduate recruitment.