Unique visitors: As its name suggests, this measure counts only the unique users who visit the site. If a particular visitor comes to the site every day, he or she counts only as a single unique.
Pages/visit: How many pages does each visitor see during a session? Higher numbers are considered better.
Average visit duration: How much time do users spend on the site during each visit? Longer is better.
Bounce rate: What is the percentage of users who view only one page on the site and then leave? Lower is better.
% new visits: This measure is the percentage of your traffic from first-time users who have never been to the site before. Generally, lower is considered better, as it means you're encouraging repeat visits.
The vast majority of websites that use an analytics tool rely on Google Analytics, for a couple of reasons. First, it's easy to use and understand. Second, it's free if your website has 10 million page views per month or less. (After that it's a hefty $150,000 a year.)
Getting started with Google Analytics is easy. When you register (a standard Google account is all you need), you receive a unique snippet of code that you then place on your website's template so that it appears on each page. Once you've done that, Google collects data every time a visitor's Web browser loads that code.
After Google has collected some data (give it a few days at least), log in to your dashboard to see a default view of your site's traffic metrics over the previous month. You'll find the traffic graph (Visits is the default) up top. Below that, links to demographic and technical data appear, including information about the language of each user.
You'll spend most of your time manipulating the graph at the top. Use the drop-down arrow next to the date to tweak the timeline you're analyzing, and use the Compare to past checkbox to overlay a past period's data. You can swap between viewing Visits, Uniques, and Pageviews (among other metrics) by using the selector beneath the Overview tab.
On the left side of the screen are additional links to more detail, which can be useful. Clicking Demographics > Location will generate a nice map of where your visitors live (don't be surprised if most are in the United States). Try using the chart type buttons beneath the graph to generate a more useful pie chart from this data.