I had observed this user behavior many times when one person go to other person desk or cubic place he or she minimize the screen windows rapidly.
When I talk to someone at my own computer, I prefer to turn and look them in the eye. If I leave what I was working on open, it can be distracting, and can prevent them from making eye-contact.
Additionally, minimizing everything (Win+D) is a quick way to show the person I'm communicating with that they have my undivided attention. Sometimes I will go so far as to lock my workstation (Win+L), but this is typically when I may need to follow the person I'm talking to.
Other times, I will minimize the screens that are not related to what the person is around to talk about. That way we can focus on the topic of discussion without being distracted by emails, and messages any more than necessary.
For me, when I do that, it's a combination of two things:
1) Hiding the screen. I may have been working on another project that the person who wandered over is unrelated to, or I may have been browsing StackExchange looking to grow my skill set, or reading a tech blog, or maybe even checking my bank balance or browsing an online shopping site if work is slow or I want to give myself a few minutes break between tasks. Odds are, if I'm in a web browser, the contents of the page are none of that person's business.
2) Giving complete attention to the person approaching. People tend to respond better if I turn away from my work and face them, giving them complete attention, despite my usual ability to multitask. When someone approaches, if I'm not doing something urgent (at which point I'll ask them to wait a few moments), I'll generally rotate my chair to face them, signalling that at the moment they're my top priority because they took the time to walk all the way over to my desk. Clearing the screen is another extension of that behavior.