In another thread the issue of Murdering Your Darlings came up, I think this deserves a thread of its own, mainly because the other thread has already been split too many ways. Many professional authors, editors, and printers give this advice, and I never really understood what they meant by it until 5 years ago when a friend read one of my stories then pointed out I overused the word and too much. They handed me back a proof read copy of one of my stories with the word and highlighted - the pages had a severe case of measles.
Since then I've tried to really limit the word and in my stories by keeping it to only one usage per sentence as a general rule - yes there are some odd times I have two of them. Most of the time where I had written and I found it was very easily replaced with other words like since, as, also, when, while, plus, then, because, and many others depending upon the context of the story and sentence. I also found I could often make a slight change to the sentence to delete an and or two. One thing I noticed once I got into the habit of doing this was the sentences became easier to read and more smooth flowing - thus a better reading story. Since then I've noticed a few other words and phrases I tended to overuse and have worked at keeping them under control.
Keeping favourite words and phrases under control is what they mean by killing off your darlings.
Now I'm sure some people will agree with me on this, while others will disagree. However, the other day I read a sentence in a story on Sol where the word and appeared nine times in a twenty-eight word sentence - it looked childish like that.
edit to replace an and with then in the first paragraph.
edit to add: the sentence I read the other day was along the lines of: I got my hat and coat and opened the door and went out to my car and opened the door and .... - If I were to rewrite that in my current style I'd make it an actions list with most of the ands replaced by commas to list the actions.