The "Cannot set headers after they are sent to the client" error occurs when trying to send multiple responses in a Node.js or Express app, typically due to modifying response headers after sending a response. To solve this issue, ensure that only one response is sent and any modifications to response headers are done before sending them. Troubleshooting steps include checking code for accidental multiple responses, verifying control flow and response operations, and using debugging tools like Jam to trace the execution flow of your code. An example code snippet is provided to illustrate how this error can happen and how it can be resolved by using `res.write()` instead of `res.send()` to send a single response.