The expected value or expectation is the (weighted) average of all the possible outcomes of an event, weighed by their probability. For example, when you roll a die, the expected value is (1+2+3+4+5+6)/6 = 3.5.
(Since a die doesn't even have a face that says 3.5, this illustrates that very often, the "expected value" isn't a value you actually expect.)