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.
Low p-value basically means how surprising your data would be if there were actually no effect (ie less than 5% of the time you’ll get this due to randomness if there is no change — which is rather impossible)
Sample size matters heavily. With more observations, estimates become more precise, so increasingly small differences can become statistically significant. With a large sample, you can therefore get a tiny, practically meaningless effect with a very small p-value.
Eg effect of $1 can be statistically significant (not random) which does not matter in practical terms if average is like $10000.
So the key point here is not only to look at the p-value but also at an actual change. If a drug gives you only 0.01% more hair, it doesn’t matter to you that it is guaranteed.
Similar things are true of Bayesian stats, leading to things like predictively oriented posteriors being studied nowadays.
Now: the p-value is the probability of you getting a result at least this extreme assuming the null hypothesis (that there is no difference in average height between the general population of French and Swedish people).
I’m also pretty sure I would fall in the camp of saying “nope don’t understand P values” as I can’t remember anything else about them.
So I admit I only know that P values are somewhat useful some of the time.