A trustless system eliminates the need for participants to know or trust each other for the system to work. Trustlessness means no central figure (like a bank) has authority or control over the said system.
Bitcoin is trustless because Bob can send Tina 1 Bitcoin without the need for a financial intermediary to oversee the transaction. Bob can use the blockchain to be certain the transaction is valid, eliminating the need to “Trust” Tina or an intermediary.
The term “Trustless” is a little misleading as a blockchain does not eliminate trust; it just minimizes the amount of trust needed and distributes it across a network of people.
A permissionless system lets anyone participate and does not require an application and approval from a central authority, like a bank, to use the services on the blockchain. Permissionless systems are synonymous with the ideas of transparency, decentralization, and accessibility. Bitcoin and Ethereum are the best-known examples of permissionless blockchains.