May be diagnosed or not, but implies that the individual learns in a way that may be outside of what is considered the "norm". In many cases, the brain is wired differently. The difference may be language or non-language based. This difference usually has nothing to do with intelligence. Cognitive abilities can range from below average to very superior but a learning disability is categorized by a wide discrepancy between cognitive ability and performance. Depending on the attitude and/or resources of a school, many students with mild to moderate "differences" can thrive in a mainstream setting.
Dyslexia, dyscalculia, dysgraphia—many different learning issues fall under the umbrella of “learning disabilities.” This video from the National Center for Learning Disabilities describes them. It also explains what issues don’t fall under that umbrella.