When you resize an image and do not resample it, you change the size of the image without changing the amount of data in that image. Resizing without resampling changes the physical size of the image without changing the pixel dimensions in the image. No data is added to or removed from the image. When you deselect, or turn off, Resample, the pixel dimension fields are not available. The only two values you can change are the physical size (Width and Height in Document Size) or the resolution (pixels/inch). When you resize without resampling, you can set either the physical size, or the resolution of the image. To keep the total amount of pixels in the image the same, Photoshop compensates for the value you set by increasing or decreasing the other value. For example, if you set the physical size, Photoshop changes the resolution.
When the pixel dimensions are constant and you decrease the physical size of an image, the resolution increases correspondingly. If you decrease the physical size of an image by half, the resolution doubles. Twice as many pixels can fit into the same space. If you double the size of an image, the resolution decreases by half, because the pixels are twice as far apart to fit the physical size.
For example, an image is 400 x 400 pixels, has a physical size of 4 x 4 inches, and has a resolution of 100 pixels per inch (ppi). To reduce the physical size of the image by half without resampling, you set the physical size to 2 x 2 inches. Photoshop increases the resolution to 200 ppi. Resizing the image this way keeps the total number of pixels constant (200 ppi x 2 x 2 inches = 400 x 400 pixels). If you double the physical size (to 8 x 8 inches), then the resolution decreases to 50 ppi. Adding more inches to the image size means that there can only be half as many pixels per inch. If you change the image resolution, the physical size changes as well.
Important: The pixel dimensions control the amount of data, and the resolution and the physical size are used only for printing.
Note: Pixels per inch (ppi) is the number of pixels in each inch of the image. Dots per inch (dpi) relates only to printers, and varies from printer to printer. Generally, there are 2.5 to 3 dots of ink per pixel. For example, a 600-dpi printer only requires a 150- to 300-ppi image for best quality printing.
For more information about the options in the Image Size dialog box, see About pixel dimensions and printed image resolution in Photoshop Help.