If $A$ is a local ring, its henselization $i:A\to A^h$ is always injective and even faithfully flat.
The rings $A$ and $A^h$ have the same dimension and share many properties :
$A$ is noetherian (resp. reduced, resp. a normal domain) $\iff$ $A^h$ is noetherian (resp. reduced, resp. a normal domain).
And if $A$ (and thus $A^h$ ) is noetherian we can add that $depth(A)= depth(A^h)$ and that :
$A$ is regular (resp. Cohen-Macaulay) $\iff $ $A^h$ is regular (resp. Cohen-Macaulay).