The answers above are mostly correct, but not completely so.
In general exp(bi) is the estimate of odds(x+1)/odds(x). This can be shown with some simple arithmetic. As Alex noted, for the dummy in question, white is 1 and non-white is 0, so we can think about this as x+1 and x, when x = 0.
As such, if exp(bi) were 0.6, then:
odds(white)/odds(non-white) = 0.6
odds(white) = 0.6*odds(non-white)
which means the odds of being a smoker are 40% lower for white than non-white.
That does not mean that a white person is 40% less likely (that is ambiguous, but I assume they mean that the probability is multiplied by 0.6, not that 40% is subtracted off, but neither is true) to be a smoker. To see what it actually means, we need to know what the probability of a non-white person smoking is.
If, for example, it's 75%, then:
prob(smoke|non-white) = 0.75
odds(smoke|non-white) = 0.75/(1-0.75) = 3
odds(smoke|white) = 0.6*3 = 1.8
prob(smoke|white) = 1.8/(1.8 + 1) = 0.642
This means that the probability has been reduced by just 14.3% (0.642/0.75 = 0.857).
Whereas, if it's 50%, then:
- prob(smoke|non-white) = 0.50
- odds(smoke|non-white) = 0.50/(1-0.50) = 1
- odds(smoke|white) = 0.6*1 = 0.6
- prob(smoke|white) = 0.6/(0.6 + 1) = 0.375
This means that the probability has been reduced by 25% (0.375/0.5 = 0.75).
In fact, we only approach "40% less likely" in the limit as prob(smoke|non-white) goes to 0.
It's very common to use "odds" and "chance" interchangeably in conversation, but they are actually two very different things. It's one of the limits/challenges of logistic regression.