What Is a Blockchain Ledger? How Crypto Keeps Score

A ledger is just a list of transactions. A blockchain ledger is that same list, kept by thousands of computers at once instead of by one bank, and written so that old entries are extremely hard to change. Every bitcoin and every ether that exists is, in the end, a line in such a list.
Who keeps the ledger?
Anyone who wants to. Picture a shared household spreadsheet where every flatmate keeps their own copy: when someone adds a line, the others compare notes, and a copy that disagrees with the rest is ignored. On Bitcoin, new lines are gathered into a block about every ten minutes. On Ethereum it is about every twelve seconds. Each block carries a fingerprint of the block before it, which is where the word chain comes from.
Why can't someone quietly edit it?
Change one old line and its fingerprint changes, which breaks the fingerprint stored in the next block, and in every block after that. To make the edit stick, you would have to redo all of that work faster than the rest of the network can add new blocks. That is what people mean when they call the record immutable: not that editing is forbidden, but that it is impractical.
Can you read it yourself?
Yes, and this surprises most beginners. Tools called block explorers, such as Etherscan for Ethereum or mempool.space for Bitcoin, show every transaction in public, forever. Paste in a wallet address and you see its whole history. Keep that in mind before assuming crypto is anonymous. It is pseudonymous: your name is not attached, but the trail is permanent and anyone can follow it.
Something practical to try: after your first transfer, look it up on a block explorer and watch the confirmations tick upwards. It turns "did it arrive?" into something you can check yourself in seconds, without asking anyone. For more depth, read how blockchain technology actually works.