This dialog is used for changing dimensions of a printed image and its resolution. It doesn't change the number of pixels in the image; it doesn't resample it (if you would like to change the size of an image by resampling it, you should use the Scale Image function instead.
Output resolution determines the number of pixels that will be used in every inch of the printed image (or another length unit, depending on your preference). You must not mistake the output resolution with the printer resolution which is expressed in dpi (dots per inch): several dots are necessary to print a pixel.
You can set the required dimensions in the Height and Width fields or the required resolution in the X/Y resolution fields. You can use different units for both printing dimensions and resolution in the drop down lists. Vertical and horizontal dimensions (and resolutions) are kept in a constant proportion by default, you can unlink them by clicking on the Chain icon.
The resolution proposed by GIMP is the resolution of the original image. If you increase the output resolution the printed image will be smaller since more pixels are used for an inch. Conversely and for the same reason resizing modifies resolution.
Increasing resolution results in increasing the printed image sharpness. This is quite different from simply reducing the image size by scaling it since no pixels (no image informations) are removed.