Statistical significance

...is not a measure of confidence in the point estimate; it says nothing about accuracy.

Statistical significance simply means that the true value of the statistic being estimated has a higher than 5% or 1% probability (the levels conventionally chosen) to be away from a range around zero (the range being determined by sample size and degrees of freedom of the estimator in question). Any statistic which is large enough will be found to be statistically significant even in small samples; this doesn't mean, however, that the accuracy of the point estimate can't be very poor.