Remix provide you with three environments to run your smart contract code. As well explained in the docs,
page reload will restart a new blockchain from scratch, the old one
will not be saved.
Injected Provider: Remix will connect to an injected web3 provider. Mist and Metamask are example of providers that inject web3, thus can
be used with this option.
Web3 Provider: Remix will connect to a remote node. You will need to provide the URL address to the selected provider: geth, parity or
any Ethereum client.
If you want the code run in a actual node, either you should run your own node and open a rpc endpoint (in geth using
--rpc flag) and provide the url for the endpoint after selecting Web3 Provider option as environment in run tab
use injected web3. E.g. have metamask extension installed in your browser and create an account and select a network (Ethereum main net or any other testnet.)