Open-source Intelligence (OSINT), also known as passive information gathering, is the process of collecting public information about a target without actually directly interacting with said target.
When this is definition is strictly followed, OSINT is undetectable and maintains a high level of secrecy due to its passive nature. If we only rely on third parties and never connect to the target's servers or applications directly, then there is no way for them to know that open-source intelligence is being conducted on them.
However, this is often quite limiting so we usually do allow for some direct interaction with the target but only as a normal user would. For example, if the target allowed us to register an account, then we would. But we wouldn't immediately start fuzzing input fields at this stage.
The importance of open-source intelligence cannot be overstated - it is, in fact, sometimes the only way to bypass security.