I've spent a few mins thinking about your question. If you want to really learn something about capacitors rather then just utilize them I would suggest a project that is very useful as well as educational. Build a circuit and write a program such that the Arduino can read the capacitance value of a capacitor you wire to the 'test terminals'. You would use a digital output pin set to HIGH to start and time a constant voltage charging a capacitor through a series resistors. you would wire the resistor/capacitor junction to a Arduino analog input pin such that you can measure the caps voltage charge at any given time in the testing cycle. You would then set the output pin to LOW to discharge the cap prior to starting another measurement cycle.
You might use several different digital outputs using different value series resistor wired to the cap and then ground. This would allow for larger capacitance measurement range. Turning on only one digital output pin at a time (the others need to be turned into digital inputs pins to not effect the charge time).
Anyway do a search on capacitor R/C time constant and then start thinking on how you can use software to time how long it takes the cap to charge to a certain value voltage and how you calculate the resulting capacitance and how you may display the results.
I think you would find it both challenging and educational as well as ending up with a practical capacitor measurement instrument.
Lefty