What exactly is L in a Cobb-Douglas production function?

Cobb-Douglas is $Y = AK^{1-\alpha}L^{\alpha}$. What exactly is $L$ in Cobb-Douglas? Is $L$ the number of workers available in a single year? Working hours?

It can be both. The number of working hours are of course easier to interpret. You can also make the assumption that every employee works some fixed number of hours, say 8 per day (or 220 per month, or 38 a week, etc). In this case if you denote by $n$ the number of workers and $L$ the number of hours worked you have of course $$n \cdot 8 = L$$ and then $$A \cdot K^{1-\alpha} \cdot L^{\alpha} = A \cdot K^{1-\alpha} \cdot ( n \cdot 8 ) ^{\alpha} = 8^{\alpha} \cdot A \cdot K^{1-\alpha} \cdot n ^{\alpha} = \left(8^{\alpha} \cdot A\right) \cdot K^{1-\alpha} \cdot n ^{\alpha}.$$ So you can choose $L$ to represent either quantity as long as you take it into consideration when choosing/calibrating $A$.
(Provided that some conditions like $n \cdot 8 = L$ hold or are a reasonable approximation of reality.)