If you use that forumla in the name manager you are creating a dynamic range which uses "this sheet" in place of a specific sheet.
As Jerry says, Sheet1!A1 refers to cell A1 on Sheet1. If you create a named range and omit the Sheet1 part you will reference cell A1 on the currently active sheet. (omitting the sheet reference and using it in a cell formula will error).
edit: my bad, I was using $A$1 which will lock it to the A1 cell as above, thanks pnuts :p