A blockchain explorer is a helpful utility that enables for transaction searching and exploring on a specified blockchain. For example, Ethereum (ETH) Blockchain Explorer (etherscan.io), allows you to search the Ethereum blockchain and see all the transactions, addresses, tokens, and activities happening on the Ethereum network. If you send or receive ERC20 tokens, or interact with DApps on the Ethereum network your transactions will be recorded on the blockchain and will be visible and searchable by all.
This transparency allows you to easily audit and reconcile all your activities on the blockchain. For instance, if you send someone some ETH and forgot how much you sent, you can easily search the transaction history for your wallet address and see exactly how much you sent and where you sent it.
Note that different cryptos run on different blockchains and therefore require different blockchain explorers to view the activity on them. Here is a list of blockchain explorers for some of the most widely used cryptos: