In Frostpunk, you take on the role of a leader whose sole job is to keep your city alive. Billed as a "society survival" game, you must build a city to keep your citizens alive in a frozen wasteland. Humanity is on the brink of being totally destroyed, and it's up to you to keep this small group alive.
At its core Frostpunk is a citybuilder. You have to take into consideration things like food, resources, housing, and more as you build up the city. However, the survival element mixes things up a bit. In addition to just having a basic thriving city, you must have things like heat, and if you don't have enough food to go around ... well, it's not good. There's definitely a fail state or two.
On top of the survival elements, Frostpunk is filled with moral questions that test you as a leader. Do you sacrifice the innocence of the children in the city to put them to work? After all, the city needs their labor and they would otherwise just be sitting around and taking up resources. Decisions will come up unexpectedly, forcing you to go one way or another, often at the sacrifice to the optimization of your city. Do you sacrifice all of your humanity in the name of survival? The choices are yours, but they will have consequences all the same.
Those choices affect the citizen's hope, something you will have to monitor closely. If they have nothing to hope for, a better tomorrow beyond just mere survival, they will not only lose motivation but may lose faith in you. Just because you lead doesn't mean that you will forever. As long as you keep the balancing act of hope, happiness, humanity, and survival, you'll stay in power. If you fail in those aspects, you'll be tossed out or the city will be doomed.