Remote nodes are useful if you are not able/don't want to download the whole blockchain, but be advised that malicious remote nodes could compromise some privacy. They may track your IP address, track your "restore height" and associated block request data, and send you inaccurate information to learn more about transactions you make. Please make sure to use a node you trust (hopefully your own) and remain aware of these limitations. Users who prioritize privacy should use the wallet in advanced mode and start a local node without setting a bootstrap node. A number of public remode nodes are listed at moneroworld.com and node-o-matic
Remote nodes can also be useful if you are running a local node and want to use Monero before the blockchain download has finished. In this situation, the remote node is known as a bootstrap node. Your local node will temporarily connect to it while the blockchain is still being downloaded. When the blockchain is synced locally, your local node will disconnect from the bootstrap node. It is a reasonable trade-off for most people who care about privacy but also want the convenience of an automatic fallback option. Be aware that when using remote nodes (including a local node with a bootstrap node), nodes may track your IP address, your "restore height", and associated block request data, as well as send you inaccurate information to learn more about transactions you make. Please make sure to use a remote node you trust (hopefully your own) and remain aware of these limitations. Keep the Monero full node software operating on your computer even when you are not using the wallet to reduce the amount of leaked data. More information at https://getmonero.org/resources/moneropedia/bootstrap-node.html