Under certain regularity conditions, the maximum likelihood estimator has, asymptotically, a normal distribution with mean equal to the true parameter value, and variance equal to the inverse of the Fisher information.
The Fisher information is minus the expectation of the second derivative of the log-likelihood evaluated at the true parameter value.
Based on this, we can construct approximate 95% confidence intervals for the true parameter value based on the MLE and the observed information.
Importantly, this is an asymptotic result so is only approximate. In particular, it is a bad approximation to a 95% confidence interval when the sample size, , is small.