EDITED after next post - #4 - from Narvey
When USB connected, PICO's V_out is the power from the USB connection provided power of 5.xV going thru Diode D1 and is connected with the input for the onboard 3.3V regulator. If not connected, that is the pin that you can use to power PICO with 3.5..16V. See schema at https://github.com/espruino/EspruinoBoard/raw/master/Pico/pdf/schematic_1v3.pdf as linked from https://www.espruino.com/Pico home page under Information section.
The 3.3V output is the Espruino PICO onboard +power rail as regulated supplied by the onboard voltage regulator. It can drive up to 250mA... and gets warmer the higher the supply voltage is (as fed in on Vout). Therefore, if you have loads to drive, have an extra supply for the drivers that drive your loads and use Espruino only to supply control signals to the load drivers (BJT/MOSFET transistors,...).
TL;DR[EDITED]: Connecting the Battery on J5 / BAT_IN will power V_out / V_BAT thru the onboard MOSFET Q1. MOSFET Q1 an Diode D1 build a protection circuit for the case that power is provided thru USB and connected Battery, and - with closed jumper - pin B0 can control powerflow to J5, the usual battery connection: batter can be charged, or - more exciting - if battery is put on BAT_out (see considerations below) , the MOSFET can drive loads that are connected to J5 (the usual BAT_in / battery connection.
TL;DR[origin - still applicable]: The Diode D1 is there to prevent power going thru USB 'back' to your laptop (or whatever is USB connected) when you power PICO simultaneously thru Vout. There is though some caveat to that, because if your supplying voltage on V_ is lower than USB's 5V (more precise: lower than 4.8V), current will most likely / could flow and put load on the Diode D1 and USB power source with undesired (side) effects. Therefore, not to co-power is always safe. For simplicity and most of the time, I use the readily available USB battery banks to feed my PICO (and other USB) powered Espruino to run into issues (Note Espruino-Wifi does not have this protection like the PICO Diode D1 and must never be co-powered!)
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