Let's say you have an image and want to display it the same size regardless of your device dpi. Then you use dp to ensure this. Since the size is the same, let's say 1 cm, in the low dpi device there will be less pixels in that cm, let's say 160, thus a lower resolution image will be enough. In particular a 160x160 pixel image will be the right size.
In a higher dpi device, e.g. with 200 pixels per cm, you will need a higher resolution version, or better you can use a higher resolution image, for example a 200x200 one.
They will still e the same size, but the one in the hdpi device will have more details.
Here you find the ratios you should consider when resizing your images (many tools can do this automatically):
http://developer.android.com/training/basics/supporting-devices/screens.html
The logical density of the display. This is a scaling factor for the Density Independent Pixel unit, where one DIP is one pixel on an approximately 160 dpi screen (for example a 240x320, 1.5"x2" screen), providing the baseline of the system's display. Thus on a 160dpi screen this density value will be 1; on a 120 dpi screen it would be .75; etc.