A trustless system does not require the parties involved to trust one another. Instead of a centralised system, a trustless one uses a distributed ledger to ensure the data being transferred is accurate. It is a very prevalent system in cryptocurrency, and a core feature of Bitcoin, which works in a peer-to-peer (P2P) system and does not require trust between parties; thus, it carries out transactions in a trustless manner.
Bitcoin as a trustless system is in stark contrast to more traditional centralised systems, such as banks, where there is a single authority that conducts all transactions. Significant issues can arise with centralised systems since they act as the main access point and, thus, a single point of failure. If the centralised authority fails, users could lose their data. In a trustless, decentralised system, however, if one point fails, there are others to keep processes working smoothly.