What's the function of a static constructor in a non static class?

I've noticed that a non-static class can have a static constructor:

public class Thing
{
    public Thing()
    {
        Console.WriteLine("non-static");
    }

    static Thing()
    {
        Console.WriteLine("static");
    }
}

And when you initialize an instance of Thing the static constructor gets called first.

Output:

static

non-static

What would be the need for this? Do you use it to initialize static fields on your instance of the non-static type?

Are there any things to take into consideration when using a static constructor?