Since the blockchain lists all transactions since the very first, an explorer allows you to track past or current transactions.
Each transaction is linked to a transaction ID (Txid or hash). You can search on the blockchain explorer using this Txid. You will then get the information related to your transaction.
Bitcoin explorers make it possible to search for information contained in the bitcoin blockchain. For example, here is the page displayed during a search from the transaction https://blockchain.info (bitcoin search explorer)
1 : Search explorer
2 : Transaction number (Txid ou hash)
3 : Adress from which funds were sent
4 : Adresse to which funds are sent
5 : Number of transactin confirmations
6 : Amount sent
7 : Size of transaction in bytes
8 : Date and time of the transaction
9 : Transaction fees used in satoshi/byte