For a data scientist I ask "what's a p-value?" Both Junior and senior candidates often get this wrong. The only difference is that senior people bristle at such a simple question before also getting it wrong.
This seems like a case where "why do we use it," an "how do we use it correctly" are obvious but the definition of what it actually is is a complexity we covered once in freshman statistics and never needed again.
You don't hire a telemarketer by asking them "what is a telephone" you hire them by making sure they know how to use one correctly.
You're assuming an underlying model for the data. You have a test statistic( that estimates a model parameter) and you have a hypothesis regarding a parameter. The p-value is the probability that you get a test statistic more extreme than the one observed assuming that your hypothesis is true.
Ex. You have a sample of 1000 men's heights. You compute the sample average height as 5'9 and a sample standard deviation of 3 inches.
(Unlikely) hypothesis: the average height is 4 feet. Your p-value is the probability of getting an sample average more extreme than 5'9 given that your 4 ft height hypothesis is true. Given that the sample standard deviation is 3 inches and 5'9 is 7 standard deviations from 4ft... the p-value is going to be small, so you'll reject that.
Note: I'm leaving out details and assumptions