Interpretation of Interesting Utility Function Solving introductory microeconomics problems I have come across the following type of utility function:
$$ f(K,L) = (\alpha K^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) L^{\frac{\sigma - 1}{\sigma}})^{\frac{\sigma}{\sigma - 1}} $$

I find it slightly reminiscent of the logarithm version of the Cobb-Douglas function, but clearly the exponents don't fit with that. So the question is: How would you interpret $\alpha$ and $\sigma$ in this case?. Is $\alpha$ still the relative fraction of capital and labour? How can I think about $\sigma$?
This is the CES production function, where CES stands for constant elasticity of substitution. 

The parameter $\sigma$ captures the (constant) elasticity of substitution and $\alpha$ is the share parameter. 

The Cobb-Douglas production function can be obtained as a special case of the CES class by taking $\sigma\to1$. For proof, I'd refer you to this post.