Kvarn is a noun meaning 'mill' or 'grinder', used to refer to any kind of tool or machine that breaks a substance down into smaller pieces.
A kvarn can be small, for example a pepparkvarn (peppar mill), köttkvarn (meat grinder) or kaffekvarn (coffee grinder).
And it can also be a big piece of machinery, for example vattenkvarn (watermill), kvarnsten (millstone), or väderkvarn (that means 'windmill', and if you're confused because you thought väder meant 'weather', here's a previous Swedish Word of the Day you should check out).
If you hear the word kvarn on its own with no context, it usually refers to a windmill, and one notable example is the Stockholm restaurant Kvarnen, meaning 'The Mill', which is referred to in Stieg Larsson's Millennium trilogy and known for its menu specializing in husmanskost.
If you're in Skåne, note that the word for 'mill' in the local dialect is not kvarn but mölla.
But as a language learner, you're probably most likely to hear kvarn used in two common Swedish idioms.
Först till kvarn, literally meaning 'first to the mill', is how the Swedes say 'first come, first served'.
It comes from the longer expression den som kommer först till qvarnen [a 19th century spelling of kvarn], får först malet, meaning 'he who is first to the mill gets the first grind'.
And another useful phrase is få vatten på sin kvarn, literally meaning 'to get water in one's mill'. This phrase is used in situations where something happens to add additional support to someone's views or argument. For example, if someone is arguing for a particular policy and a study comes out showing that the policy has been successful in another area, you could say they have fått vatten på sin kvarn.
En gammal kvarn kommer att bli vandrarhem
An old windmill will become a youth hostel
Vi har ett begränsat antal biljetter och det är först till kvarn som gäller
We have a limited number of tickets and it's first come, first served