Public Tracker

A public tracker (as opposed to a private tracker) is a tracker that allows anyone to download the torrents they host without having to be registered. These types of trackers are extremely popular and lack any form of rules as far as leeching and seeding goes. Popular examples of public trackers are ThePirateBay (TPB) and KickassTorrents (KAT).

Advantages
The biggest advantage to a public tracker is that there are no rules, anyone can access the files, there are no ratio requirements to seed times enforced.

Disadvantages
There are tons of disadvantages of public trackers, most of which are addressed by private trackers, and most of it has to do with the lacking of rules. People who download files off of a public tracker aren't required to seed the content at all, this leads to a lot of users just removing the torrent from their client as soon as it has finished downloading. This means lower speeds and less retention on torrents.

Due to the mass number of people visiting public trackers (and many not being too knowledgeable as far as torrenting/computers), there are many people who take advantage of this and upload malicious and/or fake files to a tracker in hopes of tricking someone into downloading it. Although these are generally moderated, they are far too prevalent to not be weary of.

Copyright holders are able to view all the torrents being hosted on these trackers and are able to download it themselves. Due to the nature of the BitTorrent protocol, this allows "copyright trolls" to log the IP addresses of everyone connected to the swarm and swiftly send copyright notices to ISPs who (sometimes) forward them to the user who was downloading. This can be avoided by picking a good VPN or seedbox. Copyright holders are also easily able to ask for the torrent to be removed to which the host usually complies, leading to lower retention.

History
Public trackers started appearing as early as 2004 when the BitTorrent protocol started to become more popular and BitTorrent Inc was officially formed.