Horizon is an API server for the Stellar ecosystem. It acts as the interface between stellar-core and applications that want to access the Stellar network. It allows you to submit transactions to the network, check the status of accounts, subscribe to event streams, etc. See an overview of the Stellar ecosystem for details of where Horizon fits in. You can also watch a talk on Horizon by Stellar.org developer Scott Fleckenstein:
Horizon provides a RESTful API to allow client applications to interact with the Stellar network. You can communicate with Horizon using cURL or just your web browser. However, if you’re building a client application, you’ll likely want to use a Stellar SDK in the language of your client.