What's the point of visiting students? I've started a PhD recently and seen a few students from other universities visit our lab for a few days or maybe few weeks. The other university pays all expenses which many times amount to thousands of dollars. Most of the time, the visiting student gets a place, brings her/his own laptop and does research the way he does it at his university. 

What's the point of this? Couldn't the visiting student just stay at his university and discuss his research with our lab on Skype? 

One explanation I thought of is face to face networking but the cost seems to high for that. Or it may be an excuse to travel and see the world, but that's quite ridiculous. I also asked the visiting students, but they told me they didn't know.
The main goal, from my experience, is the facetime with many different people. Skype is nice, but it's primarily intended for conversations with very few people. A visit allows students to to talk to many professors and students face-to-face in a short timespan, get to know the place, interact with students in a lab, and get a sense for what the place is like, something which is impossible over the 'net.

Also, this gives the university a good chance to see what the student is like. It's easy to look good on paper and can put on a clean shirt (pants optional) for a skype interview. It's a lot harder to keep up a fake act in front of dozens of faculty and students over a one-or-two day period.