$L$ is the class of languages that are decideable in logarithmic space on a deterministic Turing machine. In other words,
L = SPACE$( \log n)$
But why $\log n$, instead of $\log^2 n$ or $\sqrt n$. This is what, I find out in the Theory of computation book by Michael Sipser Theory of computation book by Michael Sipser, Chapter 8
Logarithmic space is just large enough to solve a number of interesting computational problems, and it has attractive mathematical properties such as robustness even when mathematical model and input encoding method change.
I am not able to understand completely, how mathematical properties and input encoding are related to defining L complexity class.