Win 10 u. Java?

What does the java program do in win 10, my laptop runs without java.

There are programs programmed with java that need a "runtime environment" to work with. Mediathekview would be such a program, without installed java you can't use that. If you do not use java-based programs you do not need java itself.

Java, as well as Adobe Shockwave Flash and Adobe Acrobat Reader is a possible security hole on the computer, so you need to keep java updated.

This will cause you to be able to run Java programs. If you do not use one, then you do not need to install a Java environment.

Of course, Java as such is not a security hole. A Java browser plugin earlier. But you do not have to install this if you only want to use a Java runtime environment.

Had it installed once since I received from win 10 the note that it does not work on the laptop with win 10 I've uninstalled it again.

What did you install? Java SE 8 runs on Windows 10.

That was not it.

Java as a runtime environment is necessary to execute programs written in Java

That would be the current Java version, which you could still install classically under Windows.

What would that bring? Advantages disadvantages?

See my answer. If you do not use java applications, it would be nonsensical to install it.