Tools>sketch tools> face curves is a way to create 3-D curves out of the UV lines of a face. I never use it that way, though.
I have found that the PREVIEW for 'face curves' is invaluable for analyzing lofts and surface fills. Understanding and controlling the direction of the UV lines on a face is often the single most important factor for getting the result I want - and is always essential for eliminating ripples, flat spots, and other imperfections.
Which way should the UV lines go? Imagine that you are sanding your shape out of a block of foam, or sculpting it from clay. Imagine the direction you would push the sandpaper (or push the clay) to get the shape you are attempting (usually both along and across the model). I have found that I almost always want the UV lines of the model to go in those same directions that I would sand or sculpt a shape.
Another way to use the 'face curves' preview is for analyzing a model to aid in the construction of a patch or bridge loft. Using the 'face curves' preview to take a look at the direction of the UV lines for the start face and the end face helps me understand the direction that the bridge face needs to 'flow' to connect the two.
How to control UV lines?
Loft: The face curves always run along the loft. If they bunch up or don't flow the way you want, you can use guide curves to 'corral them' (the face curves of a face will always, in my experience, follow a guide curve)
Surface fill: I regret to say that I don't know of any reliable way to control UV direction (anyone else care to speak up?), but sometimes tweaking the boundaries of the fill help. Go from a square to a trapezoid, arc one side, etc. Splitting edges of the fill boundary sometimes helps, but I haven't found a consistent rule.
Note: If I use constraint curves on a fill, I try to put them along the U or V direction of the patch - it seems to help make the patch smoother, because the constraint is along a natural direction of flow for the patch.