I'm from the UK and I've also never heard this expression before... but as Greg has pointed out it seems to come from a phrase written by Mark Twain:
“If it’s your job to eat a frog, it’s best to do it First Thing in the Morning. And if it’s your job to eat two frogs, it’s best to eat the BIGGEST one first.”
It may be worth asking the person that originally told you the phrase to confirm, but from what is mentioned in the comments I think it's this quote.
The phrase here means that you should prioritize things by doing the most unpleasant thing first. So if you have to do something difficult or unpleasant (like eat a frog) you should do it right away (first thing in the morning) and then the job is done (so you don't have to worry about it any more).
You will probably find that a lot of people don't know this quote/phrase, so you won't be able to get the same meaning from an altered version. To make the most sense it would be best to say the quote in full if you were giving this as advice.
If someone knows about the phrase, you could use a shortened version of it. For example if your friend needs to do their homework and they don't want to, you could say "eat the frog" to mean "do it now so you don't have to worry or think about it any more". But this would only work if the person you are speaking to knows the phrase. It could actually be fun to say "eat the frog" anyway, and see if they understand, then you could explain it if they don't.