The idea behind confidence intervals is that it is not enough just using sample mean to estimate the population mean. The sample mean by itself is a single point. This does not give people any idea as to how good your estimation is of the population mean.
If we want to assess the accuracy of this estimate we will use confidence intervals which provide us with information as to how good our estimation is.
A confidence interval, viewed before the sample is selected, is the interval which has a pre-specified probability of containing the parameter. To obtain this confidence interval you need to know the sampling distribution of the estimate. Once we know the distribution, we can talk about confidence.
We want to be able to say something about \[\theta\], or rather \[\hat{\theta}\] because \[\hat{\theta}\] should be close to \[\theta\].
So the type of statement that we want to make will look like this:
\[P[|\hat{\theta}-\theta|