Lets look at three big ones....
1. Total Visitors
2. Bounce Rate
3. Referral Sites
Each does something a little different but can give you some insight into how marketing works.
Total Visitors provides information on how many visitors you receive on any given day. If you compare month to month and year to year you should find your visitors increasing if you are doing things right. If you are not you should find your general numbers decreasing. In general, the more visitors you have the more people know about your site and the more potential sales that can occur.
Additional information collected about visitors leads to more insight such as location, income, etc... Metrics are limited by the data available to them. For example, if you have an established relationship and customer code established (i.e. login from web page) you can track what your customer does. Other times you can look at locations of visitors and demographic information to gain insight.
Bounce Rate determines how long customers stay on the site. Customers that are sticky are good for business because they are looking at your website and reading its content. There are a lot of users that float in and then bounce out because its not what they were looking for.
High bounce rates could be an indication that the information in the search engines isn't reflective of the site, the wrong key words and content aren't being used properly or you have a poorly designed site. You want the right people to find your business and stick around for a while.
Referral Sites tell you where customers are coming from. If your customers are coming from a couple of sources you can better adjust your marketing efforts to target these sites better. You may also find social media sites referring which would be an indication of a strong advertisement focal point. Referral rates provide information on where you can gain more leads.