Chris Lake at Econsultancy has listed 25 reasons why he'd leave a website in 10 seconds. It's a good list.
Reason 22 (No About page)stood out for me because it has always seemed to me that people and brands either do not have these pages or have very poor ones.
As Lake says: I often visit a website simply to find out more information about the company, and whenever the About page is missing I ever so slightly lose the will to live.
From my experience, these pages present businesses with problems - usually to do with the marketing messages that need to be included. Brands do have problems articulating what they do concisely and without using jargon. My rule of thumb for this is to say it out loud and to someone else - not a colleague. If it sounds OK then it will work.
Yes, these pages are important. They are where you tell the world who you are, what you do and how you do it. If you are in business - or on the web for that matter, I am not sure why you would not do that.