What means that android smartphone (let's say Samsung J3) does not support Java? I searched on google but I didn't find explanation what it means, what is the difference between smartphones which support Java and smartphones which does not support Java? Is anybody know? Thanks!
Quoting the documentation for the site that you linked to:
Often stands for "Java ME" (the new name of J2ME, Java 2 Platform, Micro Edition). Java ME is a platform for applications running on mobile phones. These, mainly small, applications (e.g. games) can be downloaded from the Internet directly to the phone using its built-in web-browser.
What that site is referring to by "Java" is not Android apps, but old Java ME applets. Few, if any, Android devices support Java ME. Most Android devices support Android apps, and those apps can be written in the Java programming language.