When you run a Java program you need to first start the JVM, typically this is done by running an executable, on Windows this is java.exe. You can get that in lots of ways for example just giving a full path:
C:\somedir\bin\java.exe
or may having it on your PATH.
You specify as command line arguments some class files or Jar files containing class files which are your program. But that's not enough, the java.exe itself needs various other resources, not least all the Java libraries. By setting the environment variable JAVA_HOME you specify where the JRE, and hence all those runtime resources, are to be found. You should ensure that the particular Java you execute matches the setting of JAVA_HOME.
You may also need to put JAVA_HOME\bin early on your path so that if the java.exe spawns a copy of itself (for example to compile a JSP) it picks up the right version.
JAVA_HOME allows you to run any of multiple java installations. Even if you have the /usr/lib/jvm/java-1.8.0/bin/java in your PATH first, it's useful to be able to say JAVA_HOME=/usr/lib/jvm/java-1.5.0 and have the default "java" with which you run programs use the other one, instead, as a matter of an environment setting. This allows a programmer to use the java they need, even if it's not installed in a normal system location, and test or provide reverse compatibility with that alternate version. And it's not vulnerable to being reset in the PATH by another installed program, such as a major version update for java itself.
According to @dirai hereJAVA_HOME is not used by Java itself but by some third party tools like for instance Apache Tomcat. Most applications however will work without this variable being set but some could show unexpected behaviour.
To understand the purpose of JAVA_HOME environment variable, you need to first understand which programs look for and read this variable value. Some examples are: Apache Tomcat, Apache Maven, Gradle, Jenkins etc. If you notice, most of these are development tools and that's why mostly JAVA_HOME is set to point to JDK instead of JRE.
Consumer facing Java applications don't read JAVA_HOME variable and they just need to know where the JVM is located and that's why JVM location (directory) needs to be added to the PATH variable. This is automatically done for you when you install Java software. Whenever you try to run a Java application by either double clicking on the app or through command line, your operating system reads PATH variable to locate and run JVM and it doesn't look for JAVA_HOME variable.