What is a unfit parent?

A parent who is abusive both physical and mental and doesn't provide the necessities of life. Worst case scenario as I see it.

It is a legal term that is defined by the laws of that area, if in the US, it will be defined by state laws. Normally it will be one where the children are not properly cared for, and /or the children in danager. But it can be vague or specific depending on the issue at hand, and the area you are at.

What is a unfit parent?
I've been with my husband 9yrs. Married a year he has 2 children with 2 different women. I've been with his youngest son from 7months until now he'll be 6 in July the mother just got him back in Aug.2006 he was living with us until his father went to jail we wasn't married then.So I just wanted to to know do I have any rights to his son?

That is a pretty vague question, but a unfit parent, is usually a parent who lacks the skills and abilitys to provide a safe enivorment, and to be able to enforce proper dicipline, to provide food and stuff.
But that all really depends on the situation, somem parents seem unfit in someways but great in others, in order for me to help you I need more info.

No you don't have any rights to his son, you were just mothering him for a short time. If you want to adopt him, then that's a different story. This is not a good situation for a young boy, I am sorry to hear that he has been through so much, and you too.