Permissionless networks are described in full under permissionless blockchain, the entry that covers how open networks such as Bitcoin and Ethereum let anyone take part. This page explains the adjective on its own, which crypto writers apply to far more than base-layer chains.
"Permissionless" means that no central party has to approve who participates. On an open blockchain, anyone can download the software, run a node, send transactions or help validate blocks, subject only to the protocol's rules and costs. The idea is closely tied to censorship resistance and to the goal of a trustless system, in which users rely on code and incentives rather than on an operator's goodwill.
The word also describes activity built on top of these networks. Developers can deploy applications without asking anyone; users can borrow through permissionless lending protocols; and new trading or lending venues can be launched through permissionless market creation. In practice, openness is rarely absolute. Front-end websites may block certain countries, stablecoin issuers can freeze tokens, and regulators may require KYC at the points where crypto meets bank money. The opposite model, in which access is approved, is a permissioned system.