This is a difficult question. If a child has a learning disability, sometimes it can be helpful to explain they have a disorder, and that they are not just stupid/dumb. If the child is supported, and regularly has his/her talents commented on and praised, this can also help with their self esteem.
Children with learning disabilities are often aware they are "different" from their peers. They may be told they are dumb by bullies, or they may just be aware they have more difficulty completing classwork than their peers. If it is explained to them that it is not their fault, but that they have a disorder, and everyone is open about it, they can learn from an early age that there is nothing wrong with having a disability, it just makes them special.
For example, let's think about a child who has dyslexia. This child may be frustrated because s/he is having trouble reading. You can explain to this child that they are having trouble reading, not because they are stupid, but because they have a disorder called dyslexia. You can explain what dyslexia is, and discuss how many other people in the world have this disorder. End the discussion by saying that even though the child has dyslexia, and will have trouble with school work because of this, s/he is still very special because of his/her talent for painting/piano/athletics or whatever his/her talent is. Explain that having dyslexia will not stop them from achieving what they want from life.
Of course, you need to take into account the individual. S/he may not be old enough to have such a serious conversation at this stage. If you know the child, make your own decision as to whether they could handle finding out about their disability now, or if you should leave it until they are older. They should definitely be informed at some stage.
It's also important they are told they are not "dyslexic" (or whatever the disorder is) but they HAVE dyslexia. Dyslexia is not who they are, it is what they have. (I wrote a hub about this if you're interested).