Short answers, pulled from the story.
Backward compatibility is the property of an operating system, software, product, or technology that lets it interoperate with an older legacy system, or with input designed for that older system. Removing that property from a system is called breaking backward compatibility, which usually brings costs such as switching cost.
Forward compatibility is the complementary concept to backward compatibility. A forward-compatible design has a roadmap for working with future standards and products, while backward compatibility is about working with older ones.
Stereo FM broadcasts sent the sum of the left and right audio channels in one signal and the difference between them in a second signal. Mono receivers could decode just the sum signal, while stereo receivers combined both signals to separate the left and right channels.
The IBM 360/370/390/Zseries family of mainframes and the Intel x86 family of microprocessors are cited as two of the most successful examples. IBM announced the first 360 models in 1964 and Intel announced the first 8086/8088 processors in 1978, with both lineages later migrating to 64-bit systems.
Backward compatibility preserves older games that would otherwise disappear once a manufacturer stops supporting older hardware, and it lets buyers upgrade more affordably by keeping access to their existing game library. The PlayStation 2's ability to play original PlayStation software and peripherals was a key selling point in its early months, and Microsoft later added the feature for select Xbox One titles, on which players have logged over a billion hours.
Manufacturers sometimes phase out backward compatibility toward the end of a console generation to cut costs and boost sales of newer hardware. The PlayStation 3 lost PlayStation 2 compatibility after later revisions removed its onboard Emotion Engine and Graphics Synthesizer chips, and most Wii models lost GameCube compatibility in models released from 2011 onward.