We used to have this problem with the hardware on computers, too. If you had a Windows computer and an Apple display, they wouldn't hook up to each other. Apple computers and PCs used different video connectors. The keyboards and mice also had different connectors. The same was true of Unix workstations. They had their own connectors for their monitors, keyboards, and so on, and the connectors for Sun workstations were different from those for HP workstations.
While the outsides of computers are pretty standard now--you can hook up a PC monitor to a Mac and vice versa, the same for USB keyboards and mice--the insides are still just as weird as the outsides used to be. Each computer maker has their own connection for programs that want to talk to graphics, sound, keyboard and mouse, and so on.
Back in the old days we could hook up hardware from different manufacturers sometimes using adapter cables. In other cases, we had adapters that not only connected from one connector to another, but also translated the electronic signals.
For programmers that want to write programs that run on lots of different computer systems, the Java Virtual Machine (JVM) is like a bundle of adapter cables between your program and the computer system it's running on. No matter what system you are on, the JVM makes it look the same to your program:
This is why it's called a "virtual" machine. Java provides a sort of make-believe computer that we can program for. Then the JVM makes other computer systems pretend to be that make-believe computer. So programs written for that make-believe computer will run on any computer that has the JVM on it.
In this way the JVM acts like a whole bunch of adapter cables. On a Windows system it takes the oddball connector from its graphics system and adapts it to your program so that you can use familiar graphics objects and their methods. Similarly, it adapts the sound from OS X to your program, so that you can play music or sound effects. It adapts the filesystem from Unix so that you can read and write files using the same objects and methods as you would use on Windows or OS X. And so on. The JVM adapts all the major parts of a computer to your program, so that you can wrote one program and have it run on all major computer systems, rather than having to spend your time writing it over and over for different systems.
The system isn't perfect. The biggest problem has to do with how programs are "packaged" on each of the different systems. Your program will be the same, but the way you get it to act like a native program on each system for the user varies. The program itself will be the same, but it may need a "helper" file or some other item on each host system to make it look just like a program written directly for that system.
This will typically not be a concern for you as a programmer when you're starting out. And packaging your programs for each operating systems is a lot less work than learning all the ins and outs of how to program each system (or even just one of the systems.)
The JVM is such a useful tool that languages other than Java are being written to take advantage of it. Jython, for example, is a version of the python language that's written to use the JVM. It lets you write python programs that will run on any system with a JVM on it. Groovy is another such language. There's a long list of languages that run on the JVM in addition to Java.