The concept of confidence intervals

The interval covers the true parameter with a probability or the true parameter lies in the interval with a probability ?

This animation shows the concept of the confidence interval which depends on the observations: if the samples change, the interval changes too. At last we can see that the coverage rate will be approximate to the confidence level.

library(animation)
saveHTML({
    ani.options(nmax = 100, interval = 0.15)
    par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
    conf.int()
}, img.name = "conf_int", htmlfile = "conf_int.html", ani.height = 500, 
    ani.width = 600, outdir = getwd(), title = "Demonstration of Confidence Intervals", 
    description = ("This animation shows the concept of the confidence\ninterval which depends on the observations: if the samples change,\nthe interval changes too. At last we can see that the coverage rate\nwill be approximate to the confidence level."))