These modes differed how a function that expects a single value was passed a multi celled range (for example C42:C90).
With IIE, the function chose the value of the cell on the same row or column as the formula (referred to as implicit intersection)
With AE, the function is called with each cell's corresponding value and an array (not a single value) is returend. (This behaviour is also referred to as lifting)
With the introduction of dynamic arrays, AE has become the default evaluation mode.
In Excel's object model, an AE formula is read/written with range.formula2. For backward compatiblity, a formula can be forced to behave in IIE mode (implicit intersection, no spilling) with range.formula2.
Operators
Range operator
The range operator is the colon. It produces a range with the cells between the addresses on its left and right side.
TODO: application.range seems to correspond to the colon operator.
Intersect operator
The intersect operator is a space. It evaluates to the range that is common to both ranges on its left and right side.
Thus, It is possible to write formulas such as the following which calculates the sum of the number in F10:F12
=sum(F9:F12 F10:F15)
An intersection that returns an empty set is shown with the #NULL! cell error.