I took another womans man, and she forgave me?

If she cared about the man she would forgive you for HIS sake.  If she hated him she would forgive you because you gave her freedom from him.  So the real question is "What possible reason could there be for NOT forgiving you"?  That is much harder to answer.

She didn’t forgive you for your sake, she forgave you for her sake. Holding on to anger and hatred and hurt are so bad for you in so many ways, you can actually have physical side effects from carrying all that around. She forgave you because that is what she needed to do to heal and move forward in her own life. It really has nothing to do with you at all.

Perhaps she knew he was a cheater, as you were, as well.  Perhaps she thought the two of you deserved one another; I do. Perhaps she "forgave you" because now, you have experienced being cheated upon, just as she has done.  

I'm guessing his wife knows that you will be facing the same things she is dealing with right now. She knows he is a cheat, you know he is a cheat. Are you trying to convince yourself he won't cheat on you? Because he will. Enjoy.

My guess is she was relieved. You took away a cheater from her, once a cheater always a cheater. Besides, it is at least as much his fault as it is yours. I would not blame you. 

Why? Perhaps she is a bigger woman than most could be, can realise he hurt the both of you by doing this.
Perhaps she understands that, unless her husband was open to the chance to cheat, your being vulnerable and available wouldn't have been an issue. Could be she had always had a sneaking suspicion that her husband would make the move, if the opportunity arose. Could it be you are not his only "transgression" in their marriage? 
Perhaps she can understand being in that bad place, can emapthise with how that makes you open to things happening that might not if you were feeling stronger. Could be she herself had been taken advantage of at some point and understands that it wasn't where you would normally have gone. 

She's probably grateful to you for taking that cheater off of her hands.

Because she was looking for an excuse to divorce him and you provided it. Thank you sister

she did not want to hang on to a grudge and was happy to forgive you..she knew he would eventually do the same to you

Well she either didn't;t want him or she is dumb as a box of rocks

One possibility is she is a broad minded lady who understand human problems .She may have realized that after 11 years of married life her husband would have got sexually frustrated that led him to cheat her. As such she may have thought what he not getting from me let him get from elsewhere. It is a very rare human quality .Another possibility is she is so sick and tired of her husband she knowingly allowed her husband to commit adultery so that she could take legal action for separation on grounds of adultery of her husband. Both are only possibilities .  The real reason is only known to her which is a mystery.

The reasons could be many. A good many years ago I was in a similar situation. We had a neighbor who, over a period of time, had become our best friend. One day I jokingly remarked to her that it's a good thing I didn't meet her before I married my wife and as one thing led to another, we began a long torrid relationship that lasted over 2 years. I found myself seriously in love with 2 ladies at the same time which created a problem as we both were married with children. My wife found out and we had a long 3 way discussion in which we agreed to end our affair. To this day, she is still a friend. Some ladies are forgiving and I was lucky to have one of them.

Some people have immense reservoirs of maturity from which to draw. If they share any kids it could just be the best way to remain coparents so the kids don't suffer more than they should. One just hopes you've expressed your gratitude to her for not reacting as most people would. 

Wife realized husband was a worthless bum. (You can have him) kinda thinking. 

Maybe she wasn't happy with him and glad to be rid of him.

Mat be because he was actually useless in the bedroom, hence, perfect opportunity to end the marriage in order to achieve satisfaction from someone who knows what he's doing.