In the terms abject poverty and abject misery, what does abject mean?

Abject means "of the lowest degree," referring to a level at which you can't get any worse. The word also means hopeless, downtrodden, miserable, and wretched.

In Wuthering Heights, Heathcliff talks to Nelly in a hateful rant about his wife, Isabella Linton:

Now, was it not the depth of absurdity — of genuine idiotcy, for that pitiful, slavish, mean-minded brach to dream that I could love her? Tell your master, Nelly, that I never, in all my life, met with such an abject thing as she is.