The Action Log is a list of every action taken (bans, kicks, unbans, chat pauses etc) in your chat by Moderators/Administrators.
This allows people to see what happens at all times, and allows Moderators/Administrators to help you in tracking abuse or monitoring for common issues.
The Action Log can be accessed by clicking the menu icon in your chat, and then clicking on "Action Log".
Searching the Action Log
You can search the Action Log with ease. The "Action Type" dropdown box allows you to only show rank changes, bans, kicks, or unbans.
The "Advanced Filters" link lets you fine-tune your search even more.
You can even search for actions performed by a specific Moderator/Administrator, or performed on a specific user.
You can also search the text used in a kick or ban, or search for bans with a specific duration.