There are several improvements most of which mirror those introduced with the model B+:
- A smaller form factor compared to the other models (including the A),
- Improved layout (compared to the model A),
- Combined 4-pole jack for connecting your stereo audio out and composite video out (like the model B),
- Better audio. The audio circuit incorporates a dedicated low-noise power supply (compared to the Model A and B).
- Expanded GPIO, now comes with 40 GPIO pins like the B+ (the A and B models only had 26) and is compatible with the HAT standard for add-on boards. See Joan's comment below regarding the usable number of GPIO pins.
- Better power management (compared to the A + B models).
- Now uses a micro SD card (compared to the model A).
- It is also cheaper $20.
As for software you may need to be running a newer version of the Kernel and Firmware, like with the B+.
Additional info can be found on the element 14 website, and from the raspberrypi.org site