A secondary chat is a chat feed that will be on the right side of the screen. This can be used with the trigger action: "Show text 'A' with color 'B' in secondary chat." It works the same as the regular trigger action, but now text entered here will appear on the right side of the screen.
This is mainly useful for unimportant messages in SP maps, such as a score tracker (unless you don't mind having a hint taking up the width of your screen) or miscellaneous dialogue, so that you can, say for example, have dialogue from minor characters running in the secondary chat while the important lines from main characters can be easily spotted on the left side, etc.
In MP it might be useful to have the kill feed go in the secondary chat in addition to random messages (or vice versa).