The Kotlin 'when' expression checks a value against multiple cases and returns the value of the matched case. It works like a switch but produces a value that can be assigned to a variable. Each step evaluates conditions in order until one matches, then returns its value. If no cases match, the 'else' branch provides a default value. This ensures the expression always returns something. The execution table shows how different inputs lead to different returned values, and the variable tracker shows how the result variable changes accordingly. Remember, 'when' must be exhaustive when used as an expression, so always include an 'else' case if not all values are covered.