The phrase "to stand behind one's work" means to take responsibility for something that you have done, and to accept the consequences or outcomes of your actions. It implies a sense of confidence in what you have produced, and an unwillingness to shirk accountability for it. To put it simply, if someone says they are going to stand behind their work, then they are committing themselves to ensuring that whatever they have done is up to standard, and that any issues or problems will be addressed promptly and effectively.