Starting on electronics from zero - transistor timer
Spehro explained the circuit well, I will discuss troubleshooting steps. Even experienced engineers don't always design and build circuits that work the first time. Troubleshooting is a vital skill that you need to learn.

For this circuit, I would simplify it until the LED lights up.

Remove the cap to make a simpler circuit. Most likely, the LED will still be off.

Probe Q1-B with a DMM, it should be about 0.7V.

Probe Q1-C with a DMM, it should be &lt; 0.4 V.

If these are good, remove Q1 and tie D1 anode to ground. The LED should light up.

If the LED doesn't light, it is probably in backwards.

If the LED does light when connected directly, your transistor is probably wired wrong. (or, you fried it). Re-install the transistor and check the wiring carefully.