How to read the result
A crawler reads robots.txt before it fetches a page. It looks for the group whose User-agent line names it; if there is none, it uses the * group; if there is no * group either, nothing is blocked. Inside the group, every Allow and Disallow line is compared with the path of the URL, and the longest matching rule wins. When an Allow and a Disallow match with the same length, Allow wins. This tool applies exactly those rules, which are the ones Google documents, and shows you the line that decided.
Only the path and query of a URL are tested, from the first slash. A pattern can contain * for any run of characters and end in $ to mean the end of the URL, so Disallow: /*?sort= blocks every address with ?sort= in it, and Disallow: /*.pdf$ blocks addresses that end in .pdf. A Disallow with nothing after it allows everything, and a line starting with # is a comment.
Blocking a page in robots.txt keeps the crawler from fetching it; it does not keep the address out of Google. A blocked page can still be listed if other pages link to it, just without a description. To keep a page out of the results, let the crawler fetch it and use a noindex tag instead.
Common mistakes this catches
A Disallow: / left over from a staging site blocks everything. A group for a specific crawler replaces the * group for that crawler, so User-agent: Googlebot followed only by Disallow: /private/ means Googlebot ignores every rule in your * group. And a rule such as Disallow: /blog also blocks /blog-tips and /blogroll, because rules match the start of the path; write /blog/ or /blog$ when you mean the one page.