Image resizing and interpolation
In digital image processing, an image resizing changes only the array size (dimensions) of the image. It does not care about dpi. It just upsamples or downsamples the image array. 

DPI (Dot Per Inch) is considered only when the actual physical size of the displayed (or printed) image is of concern. 

When you display a scaled image on the same physical monitor, then the apparent dpi of the image content will be changing too. This is especially important on text processing with font rendering.

Some programs try to keep image physical display size the same, while scaling them or when displayed on different monitors, by incorporating a dpi parameter to be used as well.  

[edit for answer below]
In those examples from Gonzalez's book, images are considered with their physical sizes when displayed (or printed). Assuming square pixels, DPI of a physical display device is computed by 
$$ \text{DPI} = \frac{ \text{ number of horizontal pixels on the monitor}}{ \text{ horizontal length (in inches) of the monitor}} $$

for example for a typical 15.6 inches, FHD (1920 x 1080 ), 16:9 aspect ratio laptop, the DPI will be
$$ \text{DPI} = \frac{ 1920 \times \sqrt{16^2 + 9^2}}{15.6 \times 16}  = 141.212 $$

That's the DPI of the monitor. 

Physical size of a displayed image with a array size of $M \times N$ is given by 
$$ \text{H} = \frac{ M }{ \text{DPI}} $$ horizontally and

$$ \text{W} = \frac{ N }{ \text{DPI}} $$ vertically in inches...

For amonitor with a given DPI, an image with smaller array size $M,N$ will display smaller on the screen. If you upsample (aka interpolate, or scale) the image array from $M,n$ to, say, $3M, 3N$, then the displayed image size will also be tripled.

And finally; interpolation of an image (or any digital data) means computing the sigal values that's physically in between its existing samples. In that respect you are decreasing the pixel distance when you interpolate. However, interpolation will not give you new data; it will only make exsting data smoother. That's exacty why you cannot get authentic FHD video simply by interpolating from an SD original source...