Bain Marie – Simply another name for a water bath. For example, a baking dish filled with water, into which you place your cheesecake to bake. The water will slow the cooking, and make it cook more evenly, preventing the sides from burning, or setting much more quickly than the center.

Icing Sugar – Confectioner’s sugar, powdered sugar. Used to make icings, as well as to dust pastries and cakes.

Jam Sugar – “Gelling Sugar” in the U.S. Sugar with a bit of pectin and citric acid added, used for making jams and jellies.

Self-Rising/Self-Raising Flour – Flour that already has a leavening agent of some sort in it. To substitute, for every cup (120g) of flour, add 2 teaspoons of baking powder and ½ salt.

Strong Flour – See this article for more detail. Basically “Strong flour’ in the UK equates out to a flour with a higher protein percentage. Use US “Bread Flour” to substitute. Also from the linked site:

UK plain flour is typically 10% or lower protein

You can find some UK ‘strong flour’ that’s only 12g/100g of protein – that would be the same as a US All Purpose Flour!

US all-purpose flour is generally low 12% and often around 12.9% which would be most definitely be considered ‘Strong Flour’ in the UK.

9-10% protein flour makes good cakes (small crumbs).
10.5 – 11.5% makes a decent pastry and can make bread (but not great bread), 12+ to 12.9% makes an pretty good bread. High 12% makes for crusty bread after a good hard kneading – the more you knead the bread, the more you’ll get a crust and a chewy consistency.