The reason for the &"" at the end is to deal with blank cells. If you use =Table 1::A1 without the &"", any blank cells in Table 1 will show up as zeros in the other tables. The &"" at the end causes Numbers to treat the input as text, transferring what is displayed in the cell to the other table. This can change the actual values in cells, though, which is why this method is for display only.
If cell A1 has the value 1.234 in it and you have the cell formatted to one decimal place so it displays as 1.2, the formula =Table 1::A1 will bring over the entire 1.234 formatted the same as the original cell with one decimal place displayed (unless you change the formatting to something else). =Table 1::A1&"" will bring it over as 1.2 formatted as text, the rest of the number will be gone.
If cell A1 has the value 1.234 in it and you created a custom format to display it as the text "greater than one", the formula =Table 1::A1 will bring over the entire 1.234 formatted the same as the original cell but you can format it back to a number and the 1.234 will display. =Table 1::A1&"" will bring it over as "greater than one" formatted as text and the number will be gone.
An alternate formula that brings over the actual values in the cell just like the formula =Table 1::A1 but without turning blanks into zeros is =IF(Table 1::A1="", "" ,Table 1::A1) . This makes a more direct copy of the contents of the table but is not required if all you want is a table for display or printing.