Say you've saved up all your money from

• pocket change
• babysitting
• lawn-mowing
• babysitting by making the kid mow the lawn

to get something really nice. Now you can finally replace the hand-me-down computer your uncle gave you five years ago when he upgraded to a shinier laptop. You spend the better part of a Saturday afternoon moving all your bits and bobs from one computer to another. Account information configured? Check. Cute profile pic? Check. Rotating baby animal desktop background and screensaver? Double check. Now all that's left is moving over the applications.

To get the Microsoft Office Suite going, you have to dig up the disks from behind the desk (because whatever old version you have is good enough). You load it on and reboot the computer just to be safe and…

The software's corrupted. Ugh.

It might not actually be corrupted, Shmooper. Instead, it might just be incompatible with your new computer. Hey, it happens. Computer software takes a long time to make, which means that companies want to make it as compatible with different computers as possible. Just…not so compatible that you never have to upgrade. They have to pay the bills somehow.

For a long time, though, programs only worked on one specific model of computer. Since every computer had a different architecture, you had to know intimate details like how to access the disk drive and repaint the screen to show results.
(Source)

Then came the operating system. This software let you abstract away from the electrical engineering side of computers, making compatibility actually possible. Whenever you upgrade to a new PC and your old software works, it's because some software engineers somewhere modified the code to make it work for that new system.

That's compatibility.

Computer software is considered to be backwards compatible if new versions of the software work with files and data created on older versions of the same software. For example, backward compatible spreadsheet software will let you continue updating a spreadsheet you developed with the last version of your spreadsheet software, even though you're using the newer version of the software.

Forward compatibility, on the other hand, is all about older versions of software with newer formats. Any time you open up a .docx file on Word 2003, you're expecting the forward compatibility to save you from wonky things happening to the formatting or text. Even if the older version can't handle that killer WordArt you inserted, it won't have a panic attack about it. The image just might not show up.

Hey, at least it's compatible at all.