Take this option when you are not just simply trying to paste all the cell contents, formatting, formulae, etc.  This lets you select certain things to paste and as it has three ellipsis (...) after the menu name, supplies a dialog for the purpose. You can select from just pasting formulas, formats, validation, comments, etc. Of particular note here is the 'values' selection. This allows you to copy cells where the displayed 'value' is the result of an underlying formula. If you copy this and simply 'paste', Excel will paste the underlying formula, adjusting any references in the formula as necessary. By Paste Special...>Values, you simply paste the resulting 'value' to the destination cell(s), effectively 'killing' any underlying formula(e). This is also useful for 'killing' links to external sources which cause the 'This workbook contains links......do you wish to update?' message.

There is also an 'operation' area in the dialog which lets you add, multiply, subtract, divide the contents of the clipboard. This is handy if you want to raise rates by say 10%. You just need to type 1.1 in a cell, copy it and then highlight the rates, Edit>Paste Special>Values + Multiply and that's it!

If the action you want cannot be achieved in one operation, you can repeat the 'Paste special...' action to complete the actions you need.

Skip blanks allows you to ignore pasting a blank in the 'paste area' when there are blanks in your copied data, (see below).

Transpose allows you to copy a row of data and convert it into a column and 'Paste Link' will take the data you copy and paste a reference to it (Paste a formula) anywhere else in the workbook or another workbook.

If you have copied an object other than cell data with the copy command, such as a picture, etc, selecting Paste Special... will present you with a different dialog, with all the options for the object on the clipboard.