Herbert,
The difference between source and sink:
If you connect the anode of an LED to the output of a TLC555 (a CMOS version of the 555), say, with the cathode of the LED going to ground through a resistor, the LED will light when the TLC555 output is high. When the TLC555 output is high it is sourcing current to drive the LED. To do this, internally it has a transistor connected between its output pin and the positive supply voltage. The current capacity of this transistor determines how much the TLC555 can source (it's actually 10mA).
If instead you connect the cathode of the LED to the output of the TLC555 with the anode of the LED going to the positive supply through a resistor, you get an LED that lights only when the TLC555 output is low. In this case the TLC555 must sink current to turn the LED on. To do this, internally it has a transistor connected between its output pin and ground. The current capacity of this transistor determines how much current the TLC555 can sink (it's actually 100mA).
In this simple example, you can see that if you want the LED to run at 20mA, you'd better connect it between the TLC555 output and the positive supply, otherwise you'd risk blowing up the TLC555.
The A6276 has transistors to pull its outputs low, so they can sink considerable current, but there are no transistors to pull the outputs high (I think - I haven't read the datasheet). This is called 'open collector' because the collector of the pull-down transistor is not connected to anything except the output pin.
If you want to multiplex your LEDs you'll connect them in a grid and connect all the anodes to outputs that can source current and all the cathodes to outputs that can sink current.
Then to light a particular LED, you take its anode high (using a current sourcing output) and its cathode low (using a current sinking output).
If you use a 32x4 grid, with 4 columns of cathodes and 32 rows of anodes, you could connect two A6276's to the anodes and a PIC 16F84 to the cathodes, but with the following restriction: only one output of the A6276's is allowed to be low at any instant, because the 16F84 can only source enough current to drive one LED at a time from each output pin.
(Note: it won't hurt to have more than one of the A6276 outputs low because the 25mA from the 16F84 is current limited, but the LED brightness will be proportionately reduced).
So you will be able to have up to 4 LEDs on at any given time. You are going to have a problem getting the display bright enough, because a lit LED will only get 1/32 of 25mA on average.