How does MembershipProvider work?

I understand that membership is stored at the Application level (IIS) is this correct? If I create a custom membership provider and declare member variables.....

public sealed class MyMembershipProvider : MembershipProvider
{
int intval;
public int PropertyInt
{
set { intval = value; }
}
}

and then

MyMembershipProvider mp = (MyMembershipProvider)
Membership.Provider;

mp.PropertyThing = 2;

What do I have in mp? Do I have a session-specific instance of
MyMembership provider or is it a single app-wide instance?
...