Hijab for women is the covering of everything, except for the face and hands. As far as when a woman is praying, she must also wear complete hijab, whether she is in public or she is all alone.
However, our esteemed jurists mention that the feet are exempted from being covered while praying. This means that when a woman is praying, it is not wajib for her to wear socks or cover her feet, unless she is in public or there is a non-mahram male who can see her.
And Allah knows best.