The last, last thing done before the manuscript goes out the door. Generally done by someone other than the editor or writer, in order to have fresh eyes engaged. No editing involved, though there may be some querying. Can be done electronically (Word or PDF) or on hardcopy; the latter is better because the absence of screen flicker makes it easier to see everything on the page, thus reducing chance of oversight or error.
Proofing takes two forms:
“Last eyes” cold read
A thorough examination of all elements of your document prior to going to layout or press, by someone who’s never seen it before.
Comparing printer-ready pages to marked-up ones, and verifying that all changes have been made and no new errors or omissions have popped up.