rinkeby is a public test network. If you type geth help, you'll see a number of public networks you can connect to, such as rinkeby, ropsten, goerli public test networks. If you don't specify a network, geth will connect to the public main net. You can check the Private Network Tutorial to see how to set up and connect to a private network.
Many bad things may happen, here is incomplete list of them:
Anybody may sign transactions/messages with your private keys as long as you unlock them
Anybody may use resources of your node to query blockchain state (some queries could be very CPU and HDD intensive)
Anybody may use resources of your node to publish large amounts of transactions, i.e. when ...