A horizontal cleavage tear of the meniscus is a tear that is difficult to visualise under arthroscopy as it extends horizontally into the body of the meniscus, and only the 'lips' of the tear may be visible. Horizontal tears of the meniscus are usually degenerate (ie no history of injury) and occur in older people.
The knee surgeon usually confirms the presence and extent of the horizontal tear by probing it with a blunt probe.
Horizontal 'cleavage' tears of the meniscus do NOT heal well, but if not attended to they can extend and even develop into a meniscal cyst.
What happens is that the torn meniscus is a bit like an oyster. The joint fluid can enter into the horizontal space, and then as one walks the 'lips' of the tear can close like a valve, and the fluid inside can be under quite high pressure, pushing the defect from inside and making the horizontal space bigger.
Eventually the fluid pressure pushes out the edge of the meniscus into a fluid-filled sca - a cyst - which can appear as a lump in the joint margin.
What the surgeon does at arthroscopy is to shave down the 'lips' so that the valve-like action cannot occur. Usually the shaving goes up to the healthy outer edge (if things have not gone too far).