Answer
Part A - Operation described
If the push button S1 is pressed, LED1 will turn on; if push button is released, LED1 will turn off.
Part B - Operation explained
(1) When S1 is pressed, current flows through photo diode U1.
(2) U1 is a actually a LED (Light Emitted Diode), so light (photons) will be emitted and hit the Base of the the photo transistor.
(3) The photons hitting the base will begin charging up the Base and as more and more charges building up at the Base, a voltage potential is formed between the Base and Ground, therefore current will flow from Base to Ground. Let us call this current Ib, which incidentally is small, because U1 is a weak guy, and cannot generate too many photons to make a loud enough voice that transistor can clearly hear.
(4) Luckily the transistor is a clever guy. It is basically a current amplifier, amplifying the small Base current to a big current flowing from Collect to Emitter. Let us call this amplified current Ic.
(5) Now Of course Ic flows through LED1 as well.
(6) What will LED1 will now do then? Ah, it is time for me to prepare my locking down supper. Perhaps the OP can complete my story and write up his lab report, including an acknowledgement to the EE SE perhaps? :)