Here is a great video:
First crack is mostly water vapor, second crack is mostly carbon dioxide. A lot of air roasting can go too fast and blur 1st and 2nd crack together. Look at the color of the center crease. Or better yet, don't look at it -- it can be misleading as there is usually some chaff trapped there that will deceive you. Look at the surface texture as well as color.
Dark roasting drives out oils, but this is a loss -- and the oils then oxidize.
At first, roasting is endothermic as you need to push in energy to drive out water, but at first crack things flip and become exothermic and the coffee begins to roast itself. With some coffees, especially naturals, you may not hear any cracks.
If you stop the roast right at the very start of first crack, you get "Cinnamon Roast", which is drinkable but underdeveloped.
If you stop the roast in the middle of first crack, you get "City Roast". This is good if you want to be able to clearly taste origin flavors and compare different coffees.
If you stop the roast in the very end of first crack, you get "City Roast +". The beans will have no oil and you should still be able to distinctly taste origin flavors.
If you stop just before second crack, you get "Full City" ("Medium" roast) If you get a few snaps of second crack, you get "Full City +". You might get a bit of smoke and see a few tiny bits of oil on the beans. This is a popular roast level as you get a mix of origin flavor and roast flavor.
If you stop with a rolling second crack, you get "Vienna Roast". You will have plenty of smoke and the beans will have a clear sheen of oil. Little of the origin flavor is left. Indonesians beans are an exception and may maintain a clear flavor even if roasted this dark.
Beyond this we have French and Spanish roast, but I think it is a crime to roast even to a Vienna roast so I won't even talk about these. Once you get to French roast, it matters little at all what bean you began with, you are just going to have a French roast taste. I view anything in the Vienna, French and beyond territory as a "roasting accident" and reserve such beans for emergencies only.
The mistake the person new to this might make is thinking that darker roasts are better. Charbucks certainly exploits this. Darker roasts may indeed yield a darker cup with a stronger flavor, but you have to decide if burned coffee is your thing.
The caffeine content "per bean" is the same in dark and light roasts, so don't be fooled into thinking that darker roasted coffees have more caffeine. Brew methods have more to do with caffeine with cold brew having the most caffeine and espresso the least, but we are drifting off topic.
Second is "carmelization". This happens during the interval between the beans turning yellow and first crack. The Maillard reaction causes the beans to turn brown and a variety of other reactions produce the taste and aroma that we look for in roasted coffee. This stage is critical and should not be rushed.
Third is "development" and begins at first crack. First crack takes place at 370-390. Beware stalling the roast in first crack and ending up with baked coffee - which is not good. Lots of reactions occur quickly and how fast they occur is determined to a large extent by the "momentum" of the roast. The beans have enough heat to essentially roast themselves from the inside. How long this phase is allowed to continue determines the level and darkness of the roast. You only get maybe 15-30 seconds between first and second crack, so you need to pay attention.
Tom's coffee pages / tom@mmto.org