The Google itself describes the service like this: Google Analytics is an instrument of web-аnalytics of the next generation, which shows how people find your site, how they browse it through and become your clients. Google Analytics service offers a new level of availability of corporate web-analytics for advertisers, publishers and web-site owners enabling them to use the Internet resources more efficiently.

So, what does it differ from popular counters and statistics? Unlike the latter, Google Analytics offers analytics itself but not crude statistic data.
The most popular statistic packages are Webalizer, Analog, AWStats. They are free of charge and installed on 60% sites. All these counters provide crude data which can be more helpful to site administrators than site owners or marketing managers.
There are also pay statistic packages which cost from $100 to several thousands per month. There is a lot to be said about them, so, we are planning to write an article.

Analytics is an instrument, providing free reports about the work of your site.
The reports are given as graphs, percentage, summarized figures.
And if you want to consider the details, then you can delve more and more deeply to your heart's content.

Conclusion: Google Analytics is a service enabling to see what users do on your site, where they come from and what page they leave from.
But you shouldn't think that if you have installed Google Analytics on the site, new visitors will flood in. Or you will tell them where to go and where not to go.