A stock screener is a tool that helps you sift through a large number of public companies to find the stock that fits your criteria. Screeners have a range of features. Your brokerage likely has its own stock screener, as well as screeners for other types of investments.
Basic stock screener criteria cover the most common metrics. You can quickly create a list of stocks by market cap, P/E ratio, gain or loss in a specific time period, share volume traded and a whole lot more. The free stock screener at Yahoo! Finance features these, among many filter choices:

But what makes a stock screener an advanced stock screener? There is no official definition. But some screeners have different features that are more advanced. Those could be more highly technical filters and fields. And some screeners even let you use calculated fields that you create yourself.