A chain of trust is established by validating each component of hardware and software from the bottom up.
A chain of trust is designed to allow multiple users to create and use software on the system, which would be more difficult if all the keys were stored directly in hardware. It starts with hardware that will only boot from software that is digitally signed. The signing authority will only sign boot programs that enforce security, such as only running programs that are themselves signed, or only allowing signed code to have access to certain features of the machine. This process may continue for several layers.
This process results in a chain of trust. The final software can be trusted to have certain properties, because if it had been illegally modified its signature would be invalid, and the previous software would not have executed it. The previous software can be trusted, because it, in turn, would not have been loaded if its signature would have been invalid. The trustworthiness of each layer is guaranteed by the one before, back to the trust anchor.
Source: Wikipedia, May 2017