Bitcoin’s blockchain is publicly accessible to all. Tens of thousands of nodes maintain full copies of the exact same blockchain, allowing them to verify any transaction or block and prove their Bitcoin balances. A block explorer allows those who do not run a node to do the same and in a simpler way.
However, these benefits come at the cost of potential loss of privacy and the need to trust a third party. Most block explorers exist as websites, which may collect data linking your IP address, physical location, and the Bitcoin addresses you queried. Some block explorers allow users to use their service locally with their own node, bypassing the aforementioned privacy leaks.
Try out Blockstream's Explorer to browse a complete list of Bitcoin blocks and transactions. You should avoid looking up your own addresses in order to preserve your privacy.