A system is said to be completely secure when only legitimate users may access the system's resources.
The only way to make a system completely secure is to completely destroy it along with all of its data.
Since this has other negative consequences, systems are usually only made secure enough. For example, a website administrator may decide to make their website secure enough so that script kiddies will not be able to gain illegitimate access. However, a determined and wily cracker or government would still be able to overcome their security measures.