Language aptitude is a person's aptitude to acquire or learn language and thereby make language proficiency improvement. It is generally held that some people are "good at language", whilst others are not so good.
Note this isn't the same as ability. A learner can be low ability but high aptitude, although they probably won't stay at a low level for very long. Conversely, a high level student might have reached that level through hard work and persistence rather than high aptitude. Human beings on average have a natural aptitude for language!
An aptitude test attempts to measure aptitude.
This is slightly controversial. It's almost certain that language aptitude exists, but it can be difficult to measure, and it may be that differences between individuals are not particularly large. Aptitude can also be conflated with other factors, particularly motivation.