What are these cryptic numbers? I've seen them popping up sporadically during my years in IT, but I never asked what they were

Does anyone know what they are?

They are are hexadecimal (Base 16) representations of binary (Base 2) data. Binary sequences (010101....) are how all data on a computer is stored (text files, images, executables, etc.).

What we can use them for?

Hexadecimal (0F 0F 0F....) is often used to represent binary data because it is (arguably) easier to work with, assuming someone wishes to read or edit that data for some reason. For instance, 255 in binary is 11111111 but written in hexadecimal is just FF.

As one practical example of how this can be used, software crackers may examine or edit raw file data to defeat security measures put in place by a software publisher.