Only displaying the text that fits in cell?

Well there is no screenshot so I'm guessing at what you actually mean here....

If text wrap is not on and the data in a cell overflows the width of the cell, Excel will keep displaying the text over adjacent cells until it finds one with something in it. So if the cell to the right is empty, the text will overflow across it, if it's not empty, the text will stop at the right edge of the cell.

Hope that makes sense...

There is a setting to cut off the text at the right hand cell margin, even if the next cell to the right is empty. In the formatting dialog > Alignment tab > Horizontal alignment > Fill

The down side of this setting is that text that does not exceed the column width will be duplicated to fill the cell.

Another option is to paste the text onto a different sheet (or a different area of the sheet) and then use a cell reference to display it.

For example, if cell Z1 contains "This really very long string of text", then use =Z1 in cell A1 and it will cut off at the cell border.