From the Shortmystery FAQ:
When posting, avoid irrelevant quoting (e.g. entire messages or digests) and long signature files. These are wastes of network bandwidth, causing slower dowloads.
Trimming a post (or, more often, a reply) is deleting anything extraneous to the point you are trying to make with your message.
When you create a reply with most e-mail software, the message you are replying to is often automatically quoted. If you are not replying to everything in an original message, there is no need to quote the entire message. You can delete the parts you're not addressing.
Trimming also applies to the signature lines or ads added by many ad-supported e-mail services (Yahoo!, Hotmail, Netzero).
My opinion on trimming posts is similar to mine on congrats and thanks.
It makes no difference whether a post is individual or digest; trimming a post shows I take more care with it, like taking the "trouble" to send private congrats. It shows I don't want to bother others with anything irrelevant to my post. I wouldn't include anything irrelevant if I were giving a speech or writing a letter. I give e-mail the same attention.
I make it an easy-to-read dialogue. Quote the original poster in angle brackets, then give my response without brackets:
<< Text from original message. >>