It denotes a woman's name, it does not "mean" woman. If it actually meant "woman" we'd get silly meanings such as Gynea "Woman-woman", when the -ia only denotes that this is a woman's name, and not the word for woman. Similarly "daughter" is only implied, it's not an explicit part of the name. The root is Irid-, the peculiarities of the nominative case result in a reduction to
Iris.