Java came to the market by taking three editions like:
J2SE so called as Core JAVA which is the basic foundation. It is consisting basic core concepts and applications. If you want to expertise in JAVA you have to know Core JAVA first. Core JAVA is specifically used to develop standalone application or desktop application.
J2EE so called as Core JAVA, specifically used to develop web & enterprise application. At industry you will use J2EE widely for development of application. Now a days JAVA Frameworks(Spring, Hibernate, etc.) are highly demand at Industry for application development.
J2ME is specifically used to develop Mobile or device applications