Blockchain explorers are websites that allow everyone to see all the details of every transaction that goes into the blockchain. Think of them like public web directories for every single crypto transaction. Each blockchain usually has its own blockchain explorer -- like this one for Ethereum or this for Bitcoin.
To use a blockchain explorer, find the search box and enter the transaction tx identifier (aka the string of numbers and letters that identifies each transaction). Below you can see an example of an Ethereum transaction:
You can click on most elements of the block explorer and navigate between transactions and wallet addresses. Through this method, you can potentially track all the activity of any wallet and obtain the official proof that a transaction was made.
It's also useful to use a blockchain explorer to check the status of your transaction. When the status of the transaction goes from "Pending" to "Success" you know your transaction has been securely included in the most recent block!