P-values are almost always taught poorly, but it's not actually that difficult of a concept. I took statistics in high school, again in undergrad, and it wasn't until the third time in grad school that it actually made intuitive sense (thank you Julia Yang!). When you're testing a hypothesis in statistics, it's easier to formulate a "null hypothesis" which is the opposite of what you're testing, and then try to disprove that null hypothesis.

A p-value is the probability, assuming the null hypothesis is true, of obtaining a result at least as extreme as the one actually observed.

Put differently: if the null hypothesis were true, then for p=0.05 you'd see <things at least as far from the test statistic as what you just observed> at most 5% of the time.

Put differently again: If the null hypothesis you are testing is true, then for p=0.05 random sampling would not return an observation as far from the test statistic as you just observed, 95% of the time.