What the symbol || means in electronics
It means you take the parallel combination of the resistors, rather than the series value which would easily be written R1+R2.

Frequently when we use a resistive divider with two resistors R1 and R2, it's also important to know the effective impedance of the tapping point. This is given by R1||R2. From your example, it sounds like R3 is balancing the voltage drop of a bias current, that's also flowing from the tap point of R1 and R2.

I find it's easier to do the sum \$\frac{R1.R2}{R1+R2}\$ in my head, whereas on a calculator \$\frac{1}{\frac{1}{R1}+\frac{1}{R2}}\$ tends to be easier. They are equivalent.