In networking, the physical link that carries data can be one of a number of different things: wire, cable or wireless, among others. The generic term for this is "media." Binary countdown is a media access protocol. It describes a method to get a turn putting data onto the media.
Data is transported as an electric pulse. There may be many devices connected to the same wire and they can't all apply their signals onto the wire at the same time or those pulses will get intermingled. This is called collision. To avoid collision, a computer has to check that another computer is not using the wire before applying its data. If all check at the same time, they will see the media as available and all send data at the same time. Binary countdown is one method to stop this happening.
Data is transmitted in 0s and 1s -- known as binary transmission. If several nodes on a network start transmitting simultaneously, all transmit their network ID as a binary number. These numbers are compared starting at the most significant bit, which is the first number in the sequence, representing the highest value in the byte. All those containing a zero at this bit are knocked out, if there is still more than one node in contention, the next bit along is compared. Again, those with 1 stay in and those with 0 are out. This process continues along the bits of the network ID until there is only one node left and that gets control of the media.
The binary countdown method is also called bit dominance. Although, in this example, 1 always wins, the system could work equally nominating a 0 as the winner.