APNG (Animated PNG) is a new format based on and compatible with the PNG format. It was developed to overcome technicall limitations of the Animated GIFs. The APNG and PNG specs are not legally encumbered.
PNGs are superior to GIFs in many ways, but the most obvious and important are these two:
PNGs can have a full alpha channel, whereas GIFs have at most 1-bit transparency. Making a GIF with smooth edges is practically impossible if the image is not rectangular.
The maximum range of colours in a PNG image is 16 million, whereas the maximum range for colours in a GIF image is only 256 (that's 256, not thousands or millions).
Full Alpha Channel
Note how the GIF version has the ugly gray border around it. That's because the GIF had to be created for a certain background colour, and this blue was not it. The APNG looks just as good no matter what background it's on.
High Colour Depth
This is a static image, so it's easier to see. The PNG image is much more realistic because the range of colours is limited to what the human eye can see and not what the format can do: