The word hybrid can having different meaning based upon which context it is being used. In biology hybrid means cross breeding, with electrical power generation it means two or more generators supply power to a single output, or with a car it can mean that it can use both internal combustion and electric power sources.
With Microsoft technology you can create hybrid solution that can facilitate as a bridge between on premise systems and the cloud. The solution can consist of multiple components. These components can be for instance BizTalk Server 2013 and Windows Azure Service Bus Queue, Topic, or Relay. BizTalk Server 2013 offers a new set of capabilities that can bridge on-premise systems with the cloud. These capabilities are offered with the relay adapters BasicHttpRelay and NetTcpRelay, Service Bus (SB) Messaging adapter and WebHttp offering REST support.
Combining BizTalk Server 2013, the Windows Azure Service Bus and/or REST you can build multiple different kinds of hybrid solutions. You can for instance connect integrate on-premise systems with SalesForce to support your business process. See how by examining tutorials like the Integrating BizTalk Server 2013 with Salesforce (code) or Creating a Hybrid Application Using BizTalk Server 2013. These tutorials are a showcase for you learn how to leverage the BizTalk Server adapters to configure connectivity with the Service Bus or REST and build a hybrid solution.
Microsoft has built an excellent cloud platform with Windows Azure. And through innovation in products like BizTalk it provides enterprises the means to integrate their on-premise systems with the cloud. The TechNet Wiki and MSDN library can be a great resource for you to learn how to build robust and future proof hybrid solutions.