What's the difference between digital and analog audio?

I have read that analog audio is ‘tweakable’ and allows users to get out sounds from recordings that standardized digital recordings can’t. You can, in a way, personalize the listening experience. I guess this is the same as adjusting the EQ of digital audio, but this is just what I’ve read die hard analog users say. Anyway, if anyone could explain to me the differences, similarities, pros, and cons of these formats, I’d appreciate it.