Let's compare what is meant by a 95 percent confidence interval (a term used by frequentists) with a 95 percent credible interval (a term used by Bayesian practitioners).

In a frequentist framework, a 95 percent confidence interval means that if you repeat your experiment an infinite number of times, generating intervals in the process, 95 percent of these intervals would contain the parameter we're trying to estimate, which is often referred to as θ. In this case, the interval is the random variable and not the parameter estimate, θ, which is fixed in the frequentist worldview.

In the case of the Bayesian credible interval, we have an interpretation that is more in line with the conventional interpretation ascribed to that of a frequentist confidence interval. Thus, we conclude that Pr(a(Y) < θ < b(Y)|θ) = 0.95. In this case, we can properly conclude that there is a 95 percent chance that θ lies within the interval.

For more information, refer to Frequentism and Bayesianism: What's the Big Deal? (Jake VanderPlas, SciPy, 2014) at https://www.youtube.com/watch?v=KhAUfqhLakw.