It's called "Selective Color"
You don't even need to use layers or a layer mask to achieve that effect, However, it is best to apply any changes to a layer anyways.
All you need to do is convert your image to grayscale or choose Desaturate(Shift-Ctrl-U). Then in the history panel select the point before you converted it, and then use the history brush to brush over where you want to get the color back.
Or if you prefer to use a new layer and layer mask, you can make a selection around the area you want to keep the color in and make a mask from the selection. Then click the Layer thumbnail to make sure the layer and not the mask is activated, then desaturate. Everything except your selection should turn to grayscale.
You can do the same in ACR with the adjustment brush by sliding the saturation slider all the way to the left desaturating the color from the image. Then using a new adjustment brush just brush over the areas you want to bring the color back to or resaturate. You will have to adjust your brush size and feathering, and will also have to crank up the saturation, flow and density..