If this is for average users, something like "Privacy badger stops advertizers from secretly tracking your movements and activities online" be better. "browser-add[sic] on tool that analyzes sites to detect" etc. etc. is too complicated, people won't read it IMO.
"When you visit websites, your copy of Privacy Badger keeps note of the "third party" domains that embed images, scripts and advertising in the pages you visit. If a third party server appears to be tracking you without permission, by using uniquely identifying cookies to collect a record of the pages you visit across multiple sites, Privacy Badger will automatically disallow content from that third party tracker."
Words you probably shouldn't use for a layperson friendly explanation: embed, script, server, disallow, "third party" (without explaining precisely what you mean in this context). The top question on the should be broken out into a "how does it work (generally speaking)" and "how does it work (more technical)." I'm afraid people will get stuck on that say "this is too technical" and not read the rest.