What does "DC Current VCC and GND Pins" in ATmega8 datasheet mean?
To remove further confusion. There is only one Vcc pin.
AVcc is a different power domain only for the ADC Clock system and PORTC. Read the notes below the table.

This is the right answer:  


  300mA is total current into all VCC and out of all GND pins.


See also note 3.1 


  The sum of all IOL, for all ports, should not exceed 300mA.


and 


  The sum of all IOL, for ports C0 - C5 should not exceed 100mA.    


Which is for Avcc, a special power domain for the analog part, not a normal Vcc.  

The reason for these limits is the resistance in the leadframe and bondwire and metal layers on the chip itself. A high voltage over this resistance has negative effect on the capabilities of other pins. The voltage levels (VOL/VOH) and thresholds (VIH/VIL) may shift, possibly outside of the specification. It may also add more heat than the package can handle.