AllowInlineCells is an option for cells that determines if inline cells are permitted within a cell.
With the default setting AllowInlineCells True, you can create cells nested within cells. These inline cells are useful, for example, in displaying typeset expressions or graphics along with text in the same cell.
With the setting AllowInlineCells False, inline cells cannot be created inside a cell. This is the case, for example, in InputForm input cells.