Literally, 'pay a visit' means the same thing as 'visit' - to go and see somebody or something. However, there is a slight difference in normal usage. If someone says they are going to pay somebody a visit, it usually implies some specific purpose. In any sort of drama, of someone talks about paying somebody else a visit, it almost certainly implies that the visit will be unpleasant, either asking that person some questions they probably have reason not to answer, or, at worst, threatening them or harming them. In the case above, the meaning is neutral. The speaker is going to visit MI6 to get some important needed information. The visit looks like it will be polite, but very serious.

The expression "pay a visit" has been around for about four hundred years, and is part of common English. I think any confusion about it comes from thinking "pay" only applies to money. We also pay attention, pay heed, pay respect, pay compliments and pay for what we've done. :)

They mean the same thing. "Pay a visit" is an idiomatic expression that can have a forceful connotation. Your friend may invite you to visit her, and your arrival to her home will be a happy one. Conversely, the CIA officer has not been invited to visit the M16 office, and his arrival may not be pleasant for M16. The CIA officer is "Paying them a little visit."

Disclaimer: I'm not a native English speaker. I think one particular meaning of "paying a visit" deserves more attention, namely when you visit someone out of a feeling of obligation, duty or necessity. 1. "pay a visit to the bathroom/my dentist/my doctor" (necessity) 2. from my dictionary: "pay a visit to your mother" (out of obligation. not everyone will do this (always) out of a feeling of obligation, but some do) 3. pay a visit to a war memorial (duty. as if you feel you have to have visited it) 4. "while you're in [city or country] be sure to pay a visit to ..." (you really may not miss it, "you can't miss it", it's a must-see) Also I think "paying a visit" often implies a short stay, instead of a longer one. You're only in the bathroom, with your doctor and at a war memorial (or someone's grave) for a short time. Probably not hours. The meaning of "obligation" is also close to giving/paying someone "what he/she deserves". Your mother may deserve your kind attention, fallen soldiers may deserve your demonstration of respect. Someone's who's been bad *may* (according to the person who speaks) deserve some strong words, a beating, or a bullet in their head. So I think this helps explain potential "negative" meanings of paying someone a visit. I also think public officials (say the leader of a country) may "pay a visit" to some disaster area or so. http://www.foxnews.com/politics/2013/12/26/obama-pays-visit-to-troops-in-hawaii-christmas-day/

pay a visit is a common saying. i am not sure of the origins. Perhaps when you used to pay to use the toilet in a public place. pay a visit to the men's room is quite common. visit is the correct verb.