Issues in JIRA can be searched using basic and advanced searches but with certain limitations. You can use JQL functions to overcome these limitations. For example, you cannot get the user property of a user either in the basic or advanced JQL search. For this, you would need a JQL function. These JQL functions can be used in any place in JIRA where you use JQL: in the Issue Navigator, in a Saved Filter, in the Agile Board query etc.
The Jira Misc Custom Fields plugin provides some useful JQL functions for use in your advanced JQL searches. These functions are available after installing the add-on to your instance.