JRE is a shortname for Java Runtime Edition. In short it's a bunch of applications and Java libraries that are required to run Java applications. This is what you need to run a Java application.
You can download it on java.com, which is a site for people, that aren't programmers (aka normal people).
But in order to create a Java application, you need more. You need JDK, which is a shortname for Java Development Kit. You can download it on oracle.com website. Just google jdk and you should be able to find it.
JDK contains JRE, so you don't have to download it separatelly. Don't bother about these links, instead scroll lower. Here you will find a link to JDK.
After successful installation you can find JDK in Program Files slash Java folder.
As you can see, there's much more in JDK than in JRE alone.