The so called Security fence or wall is beeing built by Israel to cut off the Westbank from Israel. Sadly it does not run on the former 67 border but right through Palestinian land and villages! In Abu Dis you can see how unhuman this wall is, as it literarily cuts right through the village and cuts it off totally from Jersualem!
If you go there while Israeli soldiers are positioned there, watch out - it could get dangerous. I almost got shot at by one!
With an "western" passport it should be easy to cross even when they have put up checkpoints. Go to the other side, buy yourself a spray-bottle and write your own graffiti on the wall.
Favorite thing: To cross the wall, it's better to go in group. Look on the picture, women climb the wall together. As it separates the town in two parts, it's incredibly difficult to do such an easy thing as to go and visit friends or family living in the same town.