what is the arrow that appears against some email correspondence listing

It might tell you that you have replied to the message or that you have forwarded it, or even possibly both. I'd be hesitant to try to describe any of these as the appearance varies according to one or more of the following:

• version of Thunderbird
• theme in use
• operating system
• desktop environment (where appropriate)

Some example icons are shown and explained here: http://kb.mozillazine.org/Icons_-_Thunderbird_2

If you're using the Correspondents column then you may have an arrow that is intended to indicate whether the message was incoming or outgoing. But this column didn't exist when that web page was written.

I know that - it is the horizontal arrow immediately to the left of the name in the Correspondents column in a Storage folder

But people can't see what you are seeing nor can they read your mind.

I'd have got there quicker if you'd said Corresponents and not correspondence.

But even now you have not answered he question

I beg your pardon?

Zenos said

If you're using the Correspondents column then you may have an arrow that is intended to indicate whether the message was incoming or outgoing.