Hard sauce isn’t really a sauce, and if you really want to think of it as a sauce, you’d probably need to call it a “spooning” rather than a pouring sauce. The British name for this — Brandy Butter — is somewhat more descriptive because with a name like that, you are prepared for something that is going to have the thickness of butter.
Hard Sauce is sugar and butter creamed together. The sugar is usually brown sugar, though many recipes call for white sugar or icing sugar. A flavouring is usually added. In England it is usually brandy, but it can also be rum, or whiskey. In North America, where vestiges of prohibition still linger, it is just as likely to be something non-alcoholic like vanilla. Some recipes add a touch of cream or milk. After making the sauce, you refrigerate it to get it hard again, and then serve in a small dish, with people spooning out what they want to put on the side or on top of warm desserts. The sauce will start to melt and pool.
Hard sauces are often used to accompany Christmas Pudding.
Some people chill their hard sauce in fancy moulds, and then turn it out onto a plate for a fancier presentation.