This is something that Ed believes in, and Sally asked in the comments if I would explain it, because it sounded to her like something that is not a very good idea. I suspect what it sounds to her like it means is exactly what it does mean, but it's a fairly fertile topic.
I think most people's approach to honesty is fairly unexamined, and mostly consists in claiming to be honest, and then telling the truth or lying according to what seems like a good idea at the time. Most people are honest enough, but people who claim not to lie at all are, IMO, either self-delusional or untrustworthy. Everyone lies sometimes, as well they should.
My general view of communication is a strategic one. I really want to be understood, and to understand others, so I'm a big proponent of openness where it's possible (i.e., not always with one's parents) and appropriate (i.e., usually not at work). Honesty greatly aids in openness, in addition to its other benefits (it's easier, it lets people trust you, and it's more ethical in its own right).
But in general, I think it's important to maintain your sense of ownership of the privacy of your own mind. If you see openness as an obligation, you may (my sense is) start lying to yourself just so that you won't have to tell difficult truths to others. I really have no qualms at all about people lying about things that are not the asker's business anyway. And I have very few qualms about another class of lying - where the purpose is not to deceive, but to withhold information that would be counterproductive (to mutual goals) to share.
At the same time, my desire to understand other people makes me behave in certain ways that encourage honesty. I resolved early in life not to be possessive, for the simple reason that it makes people lie to you. This is also behind a lot of my acceptance of others. Where it isn't safe to tell the truth, almost everyone is prudent enough to lie. I try not to make people lie to me. (I often refrain from asking questions that would likely tempt someone to lie, for instance.)
I should continue this in another post.