what is the connection between the binary operation of computers and the function of transistors?

Answer 1

Transistors act like little switches. On and off. 1 and 0.
A lot of transistors work togethter to form more complex binary strings and mathmatical operations.

You can look up AND, OR, NOT, NOR, NAND, XOR gates to discover more about complex binary operations, but to simplify it, an AND gate will only turn on when both of its inputs are 1.

Truth table for AND gate.
00 = 0
01 = 0
10 = 0
11 = 1

That will basically tell you that 1 and 1 make 2, because the output is 1.