Left ventricular noncompaction is a condition of the heart where the walls of the left ventricle (the bottom chamber of the left side of the heart) are non-compacted. This causes channels (called trabeculations) to form in the heart muscle, giveing the left ventricle a characteristic 'spongy' look (a bit like honeycomb). Although it usually affects the left ventricle, it can also affect the right ventricle. It can affect the heart's ability to pump blood, and can cause arrhythmias. It may also be associated with dilated or hypertrophic cardiomyopathy.
The following diagram, courtesy of CardiomyopathyUK