For example, if you are deploying a web application with JSP, you are technically just running Java programs inside the application server. Sometimes, even if you are not planning to do any Java development on a computer, you still need the JDK installed. It is capable of creating and compiling programs. It has everything the JRE has, but also the compiler (javac) and tools (like javadoc and jdb).
The JDK is the Java Development Kit, the full-featured SDK for Java.