Aptitude usually refers to student's natural ability to learn and progress. 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 any natural ability.
Of course, aptitude could also refer to teaching aptitude, that is some teachers are naturally better at teaching than others!