The movies really didn't do this character justice. Hopefully she'll get more development in future films, but I don't think there will ever be enough love for Jane Foster.
"We need a God who understands what it means to be humbled. To be mortal. A God who knows how precious life is. How delicate. A God who struggles everyday to live a worthy life. Who suffers so that no one else will have to. A God who loves the Earth enough to die for it. I am Dr. Jane Foster. And I will not stop being The Mighty Thor."
Origins: Jane Foster was introduced in 1962, back then she was actually a nurse (in the films, she's a scientist). She worked with Donald Blake, which was the secret identity Thor used when he was on earth. During Civil War, she sided with the Secret Avengers in opposition to the Registration Act. Later, after Thor lost the ability to wield Mjolnir, she picked it up and learned to wield it herself.
Powers: While Jane Foster is a regular human, with the power of Thor's hammer she has superhuman strength, is invulnerable to most attacks and diseases, and she can wield thunder. However, using this power is contingent upon keeping possession of Thor's hammer. Without it, not only is she vulnerable to regular human weaknesses, but also the breast cancer that she was diagnosed with before becoming Thor.
"Precursor to science FACT!"
Jane Foster is a really important character in the Marvel universe. She offers a perspective that a lot of heroes don't really have: she knows why heroes are necessary, but she also understands their cost. The toll it takes being a hero is very great, and she acknowledges that. It's a difficult position to be in, but a necessary one.