For the same reason that a drawing should have no unnecessary lines, a sentence should contain no unnecessary words, a paragraph no unnecessary sentences.
Contrary to some printed content, where column inches signify importance, your users may not even SEE every word on your web page.
Words take up space, and can often be removed without altering the meaning. This reduces the “noise” level of the page and makes the useful content more prominent. Making any page shorter allows your users to scan it without needing to scroll.
What we’re advocating here mostly applies to introductions and instructions.
Web content doesn’t need verbose welcome messages that just reiterate the page title, or tell the user how great the site is.
If your site serves clearly separate purposes, it will have clearly separate sections, but don’t be tempted to write explanations at the start of each section. Once a user is happy they’ve reached the right page, they will scan down it, rather than reading it like you do a page in a book.
Regarding instructions, if a page NEEDS them, maybe it should just be redesigned.
So be ruthless and get pruning!