Non-verbal reasoning ability, as its name suggests, is a type of reasoning ability that does not involve the use of language. As such, all else being equal, individuals with language-related impairments should not be disadvantaged in this area as compared to their non-language impaired peers. 

To some, non-verbal reasoning ability is believed to be the best single indicator of general intelligence. Unsurprisingly, some brief cognitive assessments (also widely known as intelligence quotient [or IQ] tests) solely measure this ability. Even the more comprehensive tests will include subtests that measure this ability despite already measuring multiple other areas.

Many cognitive assessments measure non-verbal reasoning ability by presenting test takers with a set of stimuli with an empty space to be filled with the appropriate answer. Test takers must look at the stimuli in their entirety to identify the underlying relationships and extrapolate this to get the answer. Some cognitive assessments even include a time measure, where test-takers need to solve the problems within a stipulated duration. The idea is that a person who can solve the same problem more quickly has a stronger non-verbal reasoning ability.

That said, non-verbal reasoning ability is a broad area that is more encompassing than the way they are commonly tested. For example, the understanding and usage of analogies require this ability. It also has an impact on our ability to make sense of concepts, such as those in Mathematics and Science. As can be seen, it forms a critical component of intelligence, even if you do not agree that it is the best single indicator. No wonder it is so widely tested!