We wanted to make the Feather HUZZAH easy to power both when connected to a computer as well as via battery. There's two ways to power a Feather. You can connect with a MicroUSB cable (just plug into the jack) and the Feather will regulate the 5V USB down to 3.3V. You can also connect a 4.2/3.7V Lithium Polymer (Lipo/Lipoly) or Lithium Ion (LiIon) battery to the JST jack. This will let the Feather run on a rechargable battery. When the USB power is powered, it will automatically switch over to USB for power, as well as start charging the battery (if attached) at 100mA. This happens 'hotswap' style so you can always keep the LiPoly connected as a 'backup' power that will only get used when USB power is lost.
The above shows the Micro USB jack (left), Lipoly JST jack (top left), as well as the 3.3V regulator and changeover diode (just to the right of the JST jack) and the Lipoly charging circuitry (right below the regulator).
There's also a CHG LED next to the USB jack, which will light up while the battery is charging. This LED might also flicker if the battery is not connected.
You have a lot of power supply options here! We bring out the BAT pin, which is tied to the lipoly JST connector, as well as USB which is the +5V from USB if connected. We also have the 3V pin which has the output from the 3.3V regulator. We use a 500mA peak low-dropout regulator. While you can get 500mA from it, you can't do it continuously from 5V as it will overheat the regulator. We use this to power the ESP8266 which can draw spikes of 250+mA (although its not continuous).
You should be able to budget about 250mA current available from the regulator, which will leave plenty for the WiFi module.
If you're running off of a battery, chances are you wanna know what the voltage is at! That way you can tell when the battery needs recharging. Lipoly batteries are 'maxed out' at 4.2V and stick around 3.7V for much of the battery life, then slowly sink down to 3.2V or so before the protection circuitry cuts it off. By measuring the voltage you can quickly tell when you're heading below 3.7V
Since the ESP8266 does not have multiple ADC pins, we didn't want to 'sacrifice' one for Lipoly battery monitoring. However we do have a tutorial that mentions how to do it, using two resistors. You can check out the wiring diagram here (use the VBat pin to measure) and the code here.
If you'd like to turn off the 3.3V regulator, you can do that with the EN(able) pin. Simply tie this pin to Ground and it will disable the 3V regulator. The BAT and USB pins will still be powered