A learning disability is defined differently by different groups.  The Federal Government (in IDEA, the special education law) defines it as,

LD is a disorder that affects people's ability to either interpret what they see and hear or to link information from different parts of the brain. These limitations can show up in many ways: as specific difficulties with spoken and written language, coordination, self control, or attention. Such difficulties extend to schoolwork and can impede learning to read, write, or do math. For more general information on learning disabilities, please visit LD In-General in our LD In-Depth section.

[Source: National Institutes of Health, 1993]