When I teach writing for the web, I tell my students to keep their writing concise and to the point. To most, this often means 'short'. But, as people, we are seldom interested in 'short'. What we're interested in is 'relevance'.
Use the right structure
When you sit down to write a web page, you need to know a lot of things to get the copy right. You need to know who are writing the page for; what they will want to do or should do on that page. You need to know your subject (obviously) and these things together determine the relevance of your content.
And when you write that web page, you use a structure for your writing - let's say it's the home page of an online store - that is different than the structure of a Twitter post. You write differently because they are different types of communication. You choose the structure that fits the communication medium.
"But what about blogs? They aren't short," I hear.
Well, yes...and no. Sometimes. But, then they are a different type of communication. A blog post has a different goal than a shopping cart page, or a product listing.
Concise is still comprehensive
Beyond the fact that a blog is meant to do something different to a web page, the length of of copy is not really something I worry about, because I write the right length for the audience and for the format I'm writing for (blog, email, Tweet, web page).
When I say that web page copy should be concise, I don't necessarily mean it should be 'short'. What I mean is that it should contain ONLY the words that need to be there to get the point across, and no more.
Why? Because people only read a handful of the words you write - so whatever you put on a page had better be on-topic and related to your goals (business, SEO, visitor). Because, if they aren't, those extra words just might get in the way of the copy actually doing what it was meant to do. Persuade.
Guidelines to being more concise
To make your website copy more concise (precise) and targeted so that your readers can focus on what you need them to do, you need to just follow the basic principles of good writing:
Stick to the point - one topic per page. One point per paragraph. One idea per sentence.
Use the active voice - X does Y. Keep it simple for your readers.
Eliminate redundancy - purge those pesky errors, wordiness and general 'fluff' (e.g. 'past history' or 'free gift' or 'end result')
Focus on the content, not the technology - writing 'click here to get some more information about so-and-so' is not only focused on how to use the technology (clicking), it is passive and takes too much concentration to figure where you're supposed to do the action. Underline your links and use a different colour so people know what to do. (Seriously. Trust them.) Just focus on the content!