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The phrase "expected value" is a phrase that didn't enter the sphere of poker jargon until relatively recently. Low stakes regulars before the poker boom were certainly not discussing it, but these days it's tough to get too far into a respectable poker book or strategy subforum without seeing it loosely tossed around. In essence, "expected value" is a concept in probability that is used to describe the average outcome of a given scenario when the scenario hinges on an uncertain, probabilistic event.
Let's take a standard, unweighted coin as an example. The average outcome here is also fairly straightforward. You would expect, on average, to be paid 50 cents. But there's a little bit of a disconnect here. The 50 cents answer seems obvious here, but how did we actually get to it? It feels somewhat unintuitive because we don't ever actually get paid 50 cents. The expected value in this example is described by considering what happens when we take the scenario and repeat it many, many times - an infinite number of times in fact.
We have to do this because it takes an infinite number of flips for us to be guaranteed that we flip an equal number of heads and tails. Given that our probabilities will "work out" to be correct in the long run, we can use them to calculate the average outcome for our scenario, which inherently assumes the long run.
For the following equations, P A will denote the probability of event A happening, and amt A will denote the payout that occurs when event A happens. So we see that our intuition here served us well - the expected value is indeed 50 cents.
But what happens if we change the scenario? Do you know what the expected value is? It's likely you can still do this in your head, or that you figured out that the answer will be halfway between the two outcomes.