The activator class handles the plugin relevant activation hooks: Uninstall, activation, deactivation and installation. The "installation" means installing needed database tables.
Indexes have a maximum size of 767 bytes. Historically, we haven't need to be concerned about that.
As of 4.2, however, we moved to utf8mb4, which uses 4 bytes per character. This means that an index which used to have room for floor(767/3) = 255 characters, now only has room for floor(767/4) = 191 characters.