First of all, lets look at the different controls of the wall. In order to best illustrate this I will use a typical exterior wall condition (brick veneer on metal stud) where the core and wall centerlines are not the same.
Walls have 6 different location line possibilities (illustrated with the red dot). You can choose your preferred location line using the options bar before you place the wall or you can change it through the wall properties after placement.
Why is this important? This is important because if you need to flip your wall after placement, the wall will flip about the location line. In the event you have dimensional constraints on the wall and the wall needs to flip for any reason, Revit will push the other walls around in the model and can sometimes result in constraint errors. Sometimes these can be ignored; however, to avoid them altogether, I like to change the location line of the wall first then flip it. Usually changing the location line to the wall centerline temporarily will take care of this issue. In the illustrations below you can see how the flipping action with a dimensional constraint can push other walls around.
We've been talking about the wall grips as they relate to the wall location line, but how does one know where the exterior face of a wall is. With walls designed for the building exterior this is usually easy because you can see the different layers of the wall and the exterior finish is a dead giveaway. But what about walls that are symmetrical (i.e. metal stud walls with gwb on both sides). If you look at the controls of a wall when you select it, you will notice the flip arrows. In addition to allowing me to flip the wall, these arrows always exist on the exterior side of the wall.
This is a nice graphical reference to help locate the exterior side of walls without having to rely on looking at the actual wall construction, because lets face it, we've all probably encountered modeling where someone did not pay attention to the wall structure and build their wall with the inside out.
I hope this has been helpful.
Remember - Make it, don't fake it.