Anaphora is a funky term that essentially refers to a stylistic effect with repetition at the beginning of sentences or phrases.
Before your brain starts spinning with "what the huh?" let's look at some examples you're probably already familiar with. Note the bolded sections:
One of the most famous examples in modern times is from Martin Luther King, Jr:

I still have a dream. It is a dream deeply rooted in the American dream. I have a dream that one day this nation will rise up and live out the true meaning of its creed: "We hold these truths to be self-evident: that all men are created equal." I have a dream that one day on the red hills of Georgia the sons of former slaves and the sons of former slave owners will be able to sit down together at a table of brotherhood. I have a dream that one day even the state of Mississippi a state, sweltering with the heat of injustice, sweltering with the heat of oppression, will be transformed into an oasis of freedom and justice. I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character. I have a dream today.

Then there's one of the most famous openings to a novel, where Charles Dickens used anaphora in A Tale of Two Cities:

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair . . .

Or how about Abraham Lincoln in his second inaugural address:

With malice toward none; with charity for all; with firmness in the right . . .

A general writing rule is to avoid repetition. But as with any rule, there are exceptions, and this is one.
My critique group is great at catching weak repetition (so, not anaphora), whether it's when one of us gets redundant with concepts ("beating a dead horse; you already showed that . . . a lot") or words ("on these two pages, your characters looked twelve times").
When I find that kind of repetition, I cut it out and revise, and I suggest the same to editing clients. A great way to find repetition is to read you work aloud. Your ear will catch things your eyes don't.
But anaphora is a different animal; it's repetition with a purpose. It's used for a specific emphasis in meaning or to create a desired impact on the reader or listener.
In thinking about anaphora, I realized I used one in Lost Without You, my first published novel (*cough*now on Kindle for cheap*cough*cough*).
It's a minor moment, when Brooke falls into a lake. Greg and Russell worry at first that she's hurt herself, but

Brooke was only wet. Very wet.

I remember circling "Very wet" during revisions, wondering whether I should take it out. In the end, I kept it in for emphasis, even though I didn't realize that what I was doing had a name. In that case, I think it worked.
Once you 're aware of it, anaphora shows up a lot. Without resorting to Dr. Google, can you think of other examples of anaphora? Any favorites?

*Edited to add: In hindsight, the example from LWY technically isn't anaphora, but epistrophe, which is repetition at the end of a line.© 2011 Annette Lyon, all rights reserved