Trust is an important concept in transactions and economic interactions. Introduced via Bitcoin in 2010, it has become the foundation of cryptocurrency.
A trustless system means no single entity has authority over the system and participants do not need to rely on each other or a third party for the system to function. This property can be seen in peer-to-peer networks whereby transactional data is stored on a public blockchain, rather than with an institution or other third party entity.
By contrast, a centralised system that is not trustless would place the power to a central point in the system, i.e. an institution who are empowered to make decisions with the information they hold from its participants. Trustless systems minimize but do not eliminate trust; it distributes trust among network participants.