Confidence… not probability!
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It is summarized well in this Math StackExchange article when BruceET states the following:
Either μ lies in the interval or it doesn't. There is no "probability" about it. The process by which the interval is derived leads to coverage in 95% of cases over the long run.
In other words, the true population parameter already exists. There's not a "probability" of it being a certain value.
We can't know for certain what the population parameter is. It's often impossible to gather all the data from a given population to get that true population mean. That's why we must gauge our confidence that it lies between a range of values!
Scenario: At Crammer Nation University, Sigma Apple Pi brothers claim to get a lot of Tinder matches. You take a random sample of 35 brothers and find a sample mean of 23.2 daily Tinder matches per brother with a standard deviation of 3.2 matches. Based on this, find a 95% confidence interval for the true mean daily Tinder matches of Sigma Apple Pi brothers.
Due to limitations on time and resources, we were limited to only taking one sample.
Each of the 20 samples would produce different sample means and different confidence intervals, because each sample would be composed of different Tinder match data from different combinations of brothers.
And... a certain percentage of them would contain the true population mean! In this case, 95% (a.k.a. 19 out of 20 samples), since that's our confidence level.
Your confidence level determines what percentage of random samples of the same size would contain the true population parameter.
PRO TIP: Want more on this topic? Check out this article from Statistics by Jim!