"EvaluateNextCell" is a front end token that first selects and then evaluates the next input cell in the notebook.
This token is equivalent to the menu command Kernel Evaluation Evaluate Next Input.
This front end token moves to and then evaluates the next input cell below the current selection. When the current selection is a single input cell, it is evaluated; otherwise, the next input cell after the current selection is selected. By repeatedly using this front end token, you can evaluate all the input cells in a notebook, one at a time.
You need to use this front end token twice for each cell, once to select it and once to evaluate it. This allows you to see the next input before evaluating it, and is good for pre-programmed demonstrations.
To execute a front end token, you typically evaluate a command of the form FrontEndExecute[FrontEndToken[token]].