The files on display may be edited if you turn on Edit Mode. This is done with the Tools->Edit Mode menu. Only real files may be edited. If you are comparing versions fetched from a Revision Control system, it cannot be edited.
If an edited side has empty areas, i.e. lines that are not part of the file and only there to line up with the other side, those will be gray.
Edit mode will not allow you to enter or remove newlines freely. Only by copying blocks from other side lines may change.
By right clicking over a change's line numbers you get options to copy lines and blocks between the two sides, as well as the options to save a file.
See also Merge.