Quality Visits can be interpreted in many different ways. In the best case, these are the visits that bring in business. In simplified manner, it's the number of visits, what last some time. eg people look around in Your website.
Best free tool today to measure traffic on Your site is Google Analytics. It gives to You quite good set of traffic data, including comparisions, keyword analysis and more.
Quality Visits = Total Visits * (100% - Bounce Rate)
If Analytics reports that You had 1320 visits and bounce rate was 72%, then 72% of visitors are not staying on Your site and "bouncing back" where they came from. Only 100% - 72% = 28% of visitors were more-or-less interested and stayed on Your site long enough.
Why is important to measure Bounce rate and Quality Visits? We had 2 different 1-day campaigns, directing potentional customers to Our web-site.
Campaign A, cost U$ 1000
21 400 visits, bounce rate 60%
Campaign B, cost U$ 1300
18 300 visits, bounce rate 23%
Witch campaign was better? Answer: B, You got 1 interested visitor for $ 0,09. Cost of the potential customer in the case of A was $ 0,12 eg 26% higher cost.
Please don't mind that I mess with visits and visitors at this point. In the future we go into it, but in our case It's almost irrelevant difference.