Charging battery through relais and arduino

Q1 is a p-channel MOSFET. Here is the schematic with its terminals labeled (G = gate, D = drain, S = source):

A MOSFET turns on (allows current to flow) when the voltage between its gate and source, or Vgs, exceeds a threshold voltage, Vth. For P-channel MOSFETs, Vth is negative, which means that the gate has to be lower than the source by some amount for the MOSFET to turn on.

When Vin is high, current flows through the diode D1 to the load, making the voltage at the source approximately Vin (minus the diode drop). Since the gate is tied directly to Vin, this means that Vgs is slightly positive and Q1 remains off.

When Vin is low, the gate is pulled to ground by Rpull (a pull-down resistor). But wait, how does Q1 turn on if the source needs to be at a higher voltage than the gate, and in order for a voltage to appear at the source, Q1 needs to be on?

Well, there's a little diode at the bottom of the MOSFET symbol; this represents the body diode (sometimes called a parasitic diode), which is basically an artifact of the way the MOSFET is made. The presence of the body diode means that even when the MOSFET is off, it will only block current from flowing from the source to the drain; it will still allow current to flow from the drain to the source. Here, that's a good thing: the body diode allows current from the battery to flow from the drain to the source, bringing the source up to near the battery voltage and creating a negative Vgs voltage difference that allows the MOSFET to fully turn on.

The purpose of Q1 and D1 are to ensure that current only flows from Vin to the load or from the battery to the load, preventing reverse current from Vin to the cell or vice versa. Replacing Q1 with another diode would accomplish pretty much the same thing:

The advantage of the MOSFET is that, when it's on, there's less of a voltage drop across it compared to a diode. Less voltage drop means less power wasted, which is especially important when you're powering your load from a battery.

Surely a high side PFET connecting the battery + terminal to the 4.2V external supply is enough. I hope you aren't doing anything unsafe, I really hope you've read about thermal issues, charge currents and voltage cycles with Lipo batties.

If you have the default logic state as the 4.2V thing connected to the battery, then have the system with a pull down resistor on Pin 12. Then when Pin 12 goes high, it will turn on the NFET low-side switch to provide the 2 Ohm load, and the gate voltage of the P fet will rise and turn it off, thus allowing you to test the battery without the 4.2V thing interfering.

You can swap the logic (not recommended, unless you also detach the battery when not in use) by putting a pull-up resistor on Pin 12 and driving it low to allow the battery to charge again.