> So it's a noun that means high-born?

It's an adjective that means "high-born".

> Could it be applied to a female?

Yes. Here's an example from Agötu saga: "Ef þú ert göfug og tigin,
fyrir hví sýnir þú þig sem ambátt?" (If you are noble and high-born,
why do you appear as a servant). Here's another from Yngvars saga
víðförla: "en sú, er tignust var, skipaði sér rekkju hjá Yngvari" (but
she who was most noble went to bed with Yngvarr).