The verb form of substantiate means to provide evidence or proof for something, in order to make it more believable. This can be done through various forms of documentation, such as statistics, testimonials, expert opinions, and other types of factual information that support the claim being made.
In a legal context, the term substantiated refers to evidence that has been verified or proven in court. In everyday language, it is often used to describe something that has been confirmed through investigation or research.