What is it?
Well, most people probably think of "telling the truth" when they consider the term honesty. But it involves significantly more than just speaking the truth. Honesty is a way of "being" - both with others and with ourselves. When we are honest, not only do we speak the truth to others, but we avoid deceiving ourself - we accept reality as we find it - and test reality to verify it.
Why is it important?
It is difficult at best, to make beneficial decisions based upon faulty information or false premises. Does it help to ignore a gas gauge in our car that reads "empty" and set out on a long trip as if we had a full tank of gas? Not unless you are trying to increase your walking activity...because you will surely run out if you persist in your denial or failure to read the gauge.
Sometimes it requires courage to face and deal with reality honestly and people grow wiser, stronger and more resourceful as a result. Honesty is a significant factor in developing influence with other people. When a person is influential and dishonest you can be sure they are getting quite a lot of help (and perhaps possess raw power) to offset this defect in order to achieve and maintain high levels of influence.
Honesty is also a tremendously more efficient way of being when compared to denial or deception. Ultimately, people can lose their spouses, careers and even their freedom when they fail or refuse to function honestly in our world - and even in less dire circumstances, the amount of time, effort and money invested in corrections and rework due to a lack of honesty is significant.