J21 is is for 7-15v (actual valid input range might lower/higher, but 7-15v will work) input into the TPS62133 which provides 5v to the rest of the board. The pin closest to the edge of the board (with a square shaped solder pad on the bottom) is Ground.
J1 is for an optional themistor (just shorted together if no thermistor is present) for use when charging a 1 cell lipo battery that is hooked up to J2 (the pin with the square pad connects to the positive terminal of the battery).
Hopefully the schematic for the board will be made available soon.
Edit: Square pin on J2 is not GND it connects to the positive + terminal/lead of the battery.
also, schematics are available here: Intel® Edison Breakout Board Schematic (pdf)
I can really connect with the J21 connector a power supply with 7-15V on the Mini-Breakoutboard or is that only for the Arduino version? i doesn't found a TPS62133 on the Mini-Breakoutboard...
I see there is a new version of the MINI_EDISON_BREAKOUT_HVM_8_26.pdf released today.
Yet i think it's still need a bit more work.
#1) EN1 & EN2 are shown as options like there are jumpers on the board so that we can change it. Yet these pins are not changeable. So why show the table at all.
Since it's configured for external resistor, just show that.
#2) What is the function of J1.
#3) It shows J21 as a shorting jumper and not as a DC input, it should also show the voltage for J21.