What is meant by fractional oxidation state?
Nothing too much, really. When you have a compound like sodium tetrathionate $\ce{Na_2S_4O_6}$, if you calculate the oxidation state of sulfur, you get $\frac{5}{2}$. This means that the AVERAGE oxigation state of sulfur is $\frac{5}{2}$. In fact, the sulfurs in the compound are not equal, you have two of them with an oxidation state of $+5$, and two of them with $0$. But when you balance redox equations, you do not really care about this, and you can use the average value of $2.5$ to find the coefficients.