8-bit CPUs process information 8-bits at a time.This was the most common computer processor in the late 1970s and early 1980s.

8-bit hardware was most common from the late 1970s to the 1980s.

8-bit displays are largely obsolete today. They can display 256 colors usually from a larger palette of 12-bits  (4,096 colors) or 24-bit (16 million colors). When multiple applications are running the various palettes will be merged by using dithering (mixing the colours with dots)

8-bits per channel (the three channels total to 24-bit) are more common nowadays. sRGB is the de facto standard. It was designed to display color images on monitors, printers and the Internet but has been universally adopted on cameras, scanners and other peripherals.

8-bit was a common color depth used to represent colors in an image but today it is usually only used to save space on disk or on the Internet. For example, I regularly take screenshots and reduce the palette to 256 colours generally saving 70% of the usual file size.

8-bit-per-channel (24-bit) sRGB is also a defacto standard for imaging software as described above.

8-bit audio is rubbish. It's about the quality of an old audio casette.

8-bit cryptography is too easy to crack because the key size determines the time taken for a brute force attack. However, some encruption uses 8-bit values to generate keys with a greater bit-length.