If you look at website statistics then you're commonly given figures for different events. This page gives you some basic information about the statistics that you see. It's based on the Webalizer format, however much of the terminology applies.
The four top level statistics are Hits, Files, Visits and Pages.
If you're looking at how effective your website is then in most cases, you can ignore the hits and files. At a basic level, the number of visitors is important as is the ratio of vsitors to pages - this gives us the average number of pages that a visitor looks at. Why is this important? Because if your site is interesting then people will stay around and read more, if it's not then they will look elsewhere.
The list of top URLs gives you information on which pages in your site are getting the most attention. If most of the people are getting to your site by typing your url into the browser then the most common page will be your home page. If, on the other hand, your site is well designed and optimized then people will be arriving via search engines and inbound links that take them straight to the content that they are interested in.
Again, a good search engine presence and link profile will mean that people jump into your site at the point where it delivers the information that they want. If they are all arriving at the same page you might have hit on a trend. If they are all leaving from a certain page then that page is either telling them all they need to know (great - but what about a call to action) or it's not delivering and should be revised.
Generaly, this is not much use to the average person as it's just a list of general service providers. Occasionally, it can be resolved to a particular company. For a B2B business, this could be a hot lead.
This is where it gets interesting. Understanding where your traffic comes from is an important step toward increasing it, and hopefully search engines are a significant source. Referrers tells you this. Add to this the information about search strings, and you can start to understand what people are searching for when they come to your site. From here you can make sure that you're giving them what they want, and ensure that you're tempting / asking / begging them to do what you want when they get there.
Other than looking at the list and ensuring that the visitors that come are using browsers that your site looks great in, this list is not much use. Might also be that you've got lots of bots appearing in this list, and this might lead to an update in your settings so that your stats are more accurate.
If you are a local business then the countries will tell you if your targeting is correct. Take some of the information with a pinch of salt - a lot of places default to a .com domain which can result in it looking like a US Commercial site when it's not. Also, some Internet service provders can be missleading - there's a few that are based in Holland, and so people in the UK browsing your site look like tey are from the Netherlands.