LM339 is a quadruple op-amp IC that uses a open-collector output, which can't drive HIGH by itself so a PU resistor often connects to it with a supply.
open-collector output: output connected to ground and is a switch (NPN transistor). It can't create a HIGH voltage (near positive supply voltage) independently. Usual outputs can both push HIGH and LOW.
If Vin+ < Vin-, Vout = 0 V, Iout = 4 mA - 16 mA, output is not high impedance state, switch closed. 0 V because the voltage is sinked to ground, i.e., a path to ground so current flow exists, thus the LED is on.
If Vin+ > Vin-, Vout = 2-5 V, Iout = 0 A, output is high impedance state, switch open, sinking the output. ~5 V because the supply is blocked by the switch from the ground, i.e., no path to ground so no current flow (0 A), thus LED is off.
[D1] The 270 or 470 Ω resistor (current-limiting resistor) limits the LED's current. The LED, if “ON”, has a 1.5 to 1.9 forward voltage, but often 1.7 V. The remaining voltage in the circuit, ~3.3 V (= 5V – 1.7V) is across the current-limiting resisto. In this case 3.3 V/470 Ω = 7 mA, enough to illuminate the LED. Most LEDs operate in a range of ~6 mA - 20 mA. Lower current makes the LED dim. Higher currents make it fail prematurely.
The PU resistor provides a path to 5 V but with little current through the 4.7 kΩ.