Typically, Cold Reading is found within scams and trickery, in order to make people think you are able to determine a wealth of information about their lives. In actuality, the Cold Reader is proposing broad generalities, waiting for a visceral reaction in the recipient (if possible), and then adjusting their reading accordingly. Whilst I personally, for obvious reasons, think fortune telling and similar quackery are bunk, what is not bunk are the psychological effects Cold Reading has on people. Rather, the psychological effects are quite fascinating.
Firstly, the ability to make logical observations, based on the physical (i.e. haircut, manner of speech, age, body language etc.) is interesting. It's interesting because on the surface, you'd think guesses weren't able to so accurately evaluate people's lives, let alone guess consistently to warrant quackery professions (i.e. fortune telling). This demonstrates the overwhelming plethora of information someone's mere existence offers to the world, yet also how remarkably similar people are, all at the same time (fascinating!)
Secondly, moving into why Cold Reading is effective, we need to address the Forer effect (also called the Barnum effect). In short, tailoring information to a person, even if it's vague or generalised, causes them to think the information is accurate. This is especially true if confirmation bias is activated (wherein the Cold Reader accurately guesses what a person already thinks about themselves). The reason this effect is effective, is because people insert their own meaning into vague, generalised statements, and then have the option to confirmation bias their way into believing it. We also see this effect in politicians, wherein the politician knows that if he/she is sufficiently vague, people will insert their own meaning, *and* think the message is being tailored to them. So, when you're intentionally being vague or generalised, people actually think you're tailoring your message to them (again: fascinating!)
So profound are the effects of Cold Reading that they consistently trigger ironic results.