Interpretation of Interesting Utility Function
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.