In addition to tracking users at a session level (how many times someone accessed your site), you can also gain valuable insight by tracking “unique” users or “unique” visitors.
When tracking unique users, you will want to count how many different visitors reached your site in a given amount of time, regardless of the amount of sessions they visited. For example, a popular online Sports magazine may want to know if out of 2M visits, 1M of them were the same 500 visitors checking World Cup scores repeatedly, which they would evaluate differently than if they had 2M unique visitors.
Internet marketers can interpret this information in a variety of ways. For example, if your goal is to increase existing customer loyalty, you’d want to see the same people coming back again and again (returning visitors).
Ideally, you want to track both total visits (hence: sessions) and unique users (hence: visitors) so you can watch the two metrics over a period of time and draw useful conclusions. Most web analytics packages include this type of information and all wise conversion optimization service should offer this service as well.