Member anniversaries are essentially how long a user has been in a Discord.
What is the member anniversary channel?
The member anniversary channel is the channel where the bot will announce members' anniversaries; however, it is not required for the bot to work. If the member anniversary channel is not set, member anniversaries will not be announced.
What are anniversary roles?
Premium servers have the ability to set up to 250 anniversary roles. For instance, on a member's 5th year in a Discord server, the bot can give them the 5 Year Veteran role as a reward for being a part of the Discord for so long.
Note: In order for the bot to be able to give a user an anniversary role, this role must be below the bot's highest role and below the highest role of the user receiving the role (even admins!). The easiest way to avoid permission issues is having Birthday Bot's role at the very top of your role list.
A user left/was kicked, can you fix their join date?
Unfortunately no, member join dates are determined by Discord and not handled by the bot.