The resolution value sets the relation between the logical size of the fractal in pixels, and its physical size in centimeters or inches. Normally, the resolution is set in DPI (dots per inch), so the logical size and the physical size are related by this simple formula:
LogicalSize (pixels) = PhysicalSize (inches) * Resolution (DPI)
For example, a 1600×1200 fractal at 300 DPI is 5.33 x 4 inch or 13.5 x 10.2 cm. If you are going to print your fractal, you probably know the resolution that your printer uses. If you use that value as the Resolution setting in the Render to Disk dialog, for example, you can directly set the size in centimeters or inches.
Ultra Fractal always uses pixels internally. It will just use the resolution value to convert physical sizes to pixel values, and it will store the resolution value with the exported or rendered images. (Note that resolution values are not supported by the JPEG and Targa file formats.)
It is important to realize that when rendering, the only thing that ultimately matters is the logical size in pixels. You can always open a rendered image in Adobe Photoshop, for example, and change its resolution, which will result in a different physical size as well. The ability to specify the resolution in Ultra Fractal means that you can directly enter the desired size in cm or inch, but remember that it is just a placeholder value.
Exporting and rendering