The left hemisphere specializes in linear (serial) processing of information. For example, the person with left-brain dominance will first notice the details in a painting and then the whole. He will look for logical mathematical answers, proofs, he will work step by step understanding the foregoing. Therefore, it is easier to learn in the classroom, where knowledge is usually transmitted 'down' (from detail to generality).
The right hemisphere specializes in the composition of information, preferably the whole and less the individual components. For example, the person with right-brain dominance will first analyze the image as a whole and then look at the details. This means that the person learns much more easily when he has been informed in advance of the subject matter or has read a summary, and is therefore prepared to have the required learning framework in place.