If something breaks down, it falls apart or stops working. In this case, schizophrenics have a thought process that doesn't work. The wikipedia entry that you have quoted (http://en.wikipedia.org/wiki/Schizophrenia) continues "Common symptoms are delusions and disorganized thinking including auditory hallucinations, paranoia, bizarre delusions, disorganized speech..." These symptoms are examples of the breakdown mentioned.
a. The act or process of failing to function or continue.
b. The condition resulting from this: a breakdown in communication.
2. Electricity The abrupt failure of an insulator or insulating medium to restrict the flow of current.
3. A typically sudden collapse in physical or mental health.
4. An analysis, an outline, or a summary consisting of itemized data or essentials.
5. Disintegration or decomposition into parts or elements.
6. A noisy, energetic American country dance.
Your quote is an example of definition 3.