Testing can detect only the presence of errors, not their absence because the main goal of the testing is “to observe the behavior of the particular software and to check whether it meet its requirement expectation or not”.
Testing is a part of broader process of software verification and validation. It consists of a set of activities, where the testers try to make the software behave anomalous in order to detect or anomaly to be later fix. Testing cannot demonstrate the faults other than specified in every circumstance. It is always possible that a test have overlooked could discover further problem with the system.