To learn something off by heart is common in my part of England. Just means to learn something so that you won’t forget it, particularly for songs, poems etc.

American English omits the “off”, but it means to learn something thoroughly so you can recall it instantly.

I don't think I've ever heard "learn something off by heart". To "learn something by heart" is a very common expression that means to learn/memorise something very well. Having said that, according to some online dictionaries, it seems "learn something off by heart" is just a variation. If I were you I would stick with "learn something by heart". Examples We learned the lyrics by heart so we wouldn't need to look at them. You don't need to learn all the phrasal verbs by heart--you'll get a sense of them as you go along. I hope this helps

It should say "Lean this definition by heart" or simply, "Learn this definition."