Once you know what to look for in a curve, it tells you a lot. For example, you'll know...
Originally Posted by StoneNYC
If shadows will look dark and mushy (long toe) versus snappy (linear or downswept).
If highlights will lack gradation (downswept) or be snappy (linear or upswept).
How much overexposure you can get away with (linear on right end).
Likewise with underexposure (short toe).
You can use curves to your advantage. For example, Bill Burk mentioned that an upswept curve can improve gradation in faces. A downswept curve will let you cram a large luminance-range onto the print by compressing highlights (example: snow/sand/clouds, where you also have something dark or shadows). Downswept also will give you strong shadow-gradation which can help in low-key shots. An S-shaped curve will have snappy midtones at the expense of reduced gradation in both shadows and highlights, which might be just what's needed to strengthen a midtone-heavy scene.
Developers and agitation change the shape of curves, so you can alter curves to suit your needs. I haven't seen curves produced by Diafine, but I'd guess they're downswept.
For general usage, a straight-line curve is best because it gives equal gradation in shadows, midtones and highlights.
Anyway, it's a good idea to be familiar with the curve for your film+dev combo so you'll know what you're going to get.