Biquinary is a way of counting using just two symbols: "0" and "1". But it's a little different than the way we normally count with just ones and zeroes.
In biquinary, we group our numbers by pairs. Instead of counting up in ones like we do in normal counting (1, 2, 3, 4, 5, etc.), we count up in twos (01, 10, 11, 100, 101, etc.).
So, 01 represents the number 1 and 10 represents the number 2. When we get to the number 3, we need to group it differently. Instead of just having two digits we add a third digit and use the grouping 001 which represents three.
This counting system made it possible to represent numbers using mechanical machines. For example, some early calculators used biquinary to calculate numbers. Nowadays, we don't use biquinary as much as we use our normal way of counting (1, 2, 3, 4, etc.), but it's still an interesting way of thinking about numbers!