How does it work?
The premise is that most responses to emails in Outlook will include the original. So if Bob sends a question to Jenny, who replies to Bob and copies Carl, who then replies to both with the answer... then Carl's reply contains everything that the previous 2 messages had, so we don't need to keep them as well.
You'll find that TC is only really effective on internal mail - since it uses Outlook's conversation threading properties that are preserved for Outlook/Exchange messages but don't carry over onto mail that goes outside. If you use TC and you start seeing messages that you think *should* be compressed, but haven't ... then this is the likely reason.
Another reason for not compressing is that TC will keep messages with attachments - so if Bob's mail to Jenny had a document attached, and Jenny replies, Outlook will remove the document. TC will therefore preserve Bob's original mail within the thread.
Once you're confident in TC, you may choose to have it actively delete content. Otherwise, you could have it move "compressed" items to your Deleted Items folder or some other folder you may create (in a PST file, for example). There's also an option on the Advanced tab to have it not remove mail, but just mark it as read. Or to keep various flavours of mail (like high priority ones). Have a play. You'll figure it out.
Brief explanation of usage
Here's the standard window. TC starts in whichever folder you're viewing when you launch it, though you can use the "..." to the right of the Selected Folder, to choose a different one.
If you configure TC to use Deleted Items folder (or some other folder that you can select), it will move "compressed" items in there rather than outright deleting them.
QuickCompress is a feature which means it starts compression automatically. You may want to try that out if you use it regularly, but don't worry about it at first.
The Attachment Types section allows you to configure TC to not keep messages with attachments - eg if Bob mails Jenny and has a VCF contact attached in his email signature, TC would elect to keep Bob's mail in the thread because it has an attachment. If you wanted TC to not keep mails with just those types of attachment, then add VCF to the list.
Exceptions. Sometimes there are people whose mail you just want to keep regardless of whether it's in a thread or not. Add their names to the list.