Kissing spines is a back condition in horses that may be congenital or caused by trauma such as a serious fall. It's most often seen in shorter backed horses that are used for jumping - indicating that while it's most often conformational in course, jumping probably makes it worse. A horse has long, thin bones that protrude upward from each vertebrae - they're longest just above the shoulder, forming the withers. Sometimes these bones come into contact, causing pain or stiffness in the spine and eventually resulting in arthritis in the back.
Fortunately, it can be treated - most often by a combination of rest, medication (steroid injections are common) and physical treatment. A good chiropractor can go a long way to correct the condition by unsticking the back, and horses that have had kissing spines in the past should get regular chiropractic treatment, as it does tend to recur.