So, let's begin:
Patch - Patch is a session that has rules governing who can use the ice at that time, usually only figure skaters are able to use patch ice. You usually have to have your own skates, be at a certain level, or be having a lesson with a coach. Some rinks have other rules too.
Practice Book - A small notebook, that a coach will write notes in for a skater. This means that when the skater is not in a lesson, they can refer to the notes and have tips on technique, timing or other things. It also helps with planning what to do on a practice session, so you're not simply skating aimlessly around.
Skate UK - The UK learn to skate programme, created by NISA (more on them in a minute)
NISA - The National Ice Skating Association. The body that oversees skating in the UK.
Outside Edge - This is the edge of the blade that corresponds to the outside part of your foot.
Inside Edge - The part of the blade that corresponds to the inside of your foot.
Toepick - Found on figure skates, this is an implement to
Penguin - A penguin is a skating aid that looks like, funnily enough, a penguin. They're child height, and are designed so that children can start skating independently straight away.
If I think of any more, I'll add them to the list, but you'll hear me talk about these ones quite often.