Here’s my question, my coins are currently on binance. How important is it to put them on the ledger?
The saying is that if you don't own the private key (or seed), it's not your bitcoin.
If Binance gets bankrupt, or hacked, your coins will be lost.
If your account gets hacked (usually together with your mail address) or somebody manage to impersonate you in a way or another and get access, he may be able to withdraw your coins into his own wallet.
So the best approach is to keep your funds in your own wallet.
But it's a bit more complicated. If you have a hardware wallet (is that what you meant by ledger?) then make sure you generated yourself the wallet, make sure you have the seed written down correctly and it won't even hurt, if not a big hassle, to make sure you can recover the same wallet/addresses from the seed. Just to be extra sure.
If you don't have a hardware wallet, my advice is to keep on paper wallet the Bitcoins you don't plan to use in the next months or years. There are plenty of tutorials on how to safely generate such paper wallets. (Again, it could be good to also make sure the generated private key is for the address you expect!) And only the coins you expect to spend in the rather near future should be kept in hot wallet (wallet that's connected with the internet).
It worth mentioning that keeping safely private keys or seeds means to not keep them on the computer like "bitcoin.seed.backup.txt", clearly not in e-mail or cloud storage also. Best would be on papers, written in a way you could read it properly in 5 years too, and those papers should stay in a few different (safe) places.