A Python TypeError occurs when an operation is attempted on an object with an inappropriate data type, often resulting from incompatible data types, incorrect function inputs, or non-callable objects. Common scenarios include adding a string to an integer or using a string as a list index instead of an integer. To illustrate, attempting to add a string to an integer raises a TypeError because these types are incompatible for addition. To avoid such errors, checking the types of objects before performing operations is recommended, ensuring compatibility and supporting operations. Additionally, tools like Rollbar can help developers manage and analyze errors in real-time, making error handling in production code more efficient and less stressful.