I use MS Excel 2010. In this app, I know that using Formulas > Define names > define name it is possible to name a cell (or range). At that dialog box there is a scope rectangle which if I choose the entire sheets scope (workbook) so it's said that this name is valid for the entire workbook. First what does this valid mean please? Then, OK, I think I understand it but why when I name cell A1 (in the worksheet1 for example) to "first" its name on that worksheet is valid, that is its name, here "first", is shown in Name Box, but although I've used workbook scope, when I change the worksheet (to worksheet2) and active cell A1, just A1 is shown there not the put name, "first"!?
You've got the logic backwards...
When you set a workbook-scoped name, you are saying that "First" will always point to Sheet1!A1, no matter where in the workbook you refer to First at. In this scenario, you have not named Sheet2!A1, so no name will appear when selecting it.
If you set a worksheet-scoped name, you could set "First" to be A1 in Sheet1 (when used within Sheet1), to be B1 in Sheet2 (when used within Sheet2), etc.