To teach in China, you must abide by three basic requirements. The first is a bachelor's degree, the second is being aged 25 to 55, and the third is two years' of post-bachelor's work experience. For this third requirement, the Chinese government accepts a reference letter as proof. This reference letter is often used to assess your job application.
When you leave a job, however, it can be tricky obtaining a reference letter, especially if you've taught in another country. Often, your last employer has little incentive to provide a reference letter as it can take time to write. Furthermore, if you've already left your employer, they know that it's very unlikely that you will return. Teachers employed in Korea have a particularly difficult time obtaining a reference letter from their Korean company. This is why it's important to obtain a reference letter before you officially leave your employer. It is generally easier obtaining a letter when asking in person, instead of relaying numerous emails and telephone calls.
Remember that your resume, if written well, may give a good description of your background but it is in no way proof of your accomplishments. The Chinese government will demand a copy of your university diploma to testify your academic achievement, and will need similar proof for your professional achievements also. An employer will typically verify your diploma and references before handing them in to the government, so make sure that your reference letters list the contact details of the person writing the letter. Moreover, scanning your diplomas and reference letters (in addition to your passport photo page) will make the job search process considerably easier as employers ask for these documents by email frequently. The more seasoned ESL teachers almost always have electronic copies of their documents ready to hand!