Bulk API - The Bulk API provides programmatic access that lets you quickly load large data into your Salesforce organization.
Example - You are developing any thirdy party application, which is used to load data into salesforce through CSV file. The Bulk API provides the features to handle large set of data to load into salesforce. Refer this link to more details https://developer.salesforce.com/page/Bulk_API
Streaming API - The Force.com Streaming API lets you expose a near real-time stream of data from the Force.com platform. Administrators can create topics, to which applications can subscribe, receiving asynchronous notifications of changes to data in Force.com, via the Bayeux Protocol. Streaming data made simple, secure, and scalable.
Example - You want to display the closed case record in your page in real-time, without refreshing the page you want to display the data in realtime.Refer this link for more details https://developer.salesforce.com/page/Streaming_API
Example - You are developing any thirdy party application, which is used to load data into salesforce through CSV file. The Bulk API provides the features to handle large set of data to load into salesforce. Refer this link to more details https://developer.salesforce.com/page/Bulk_API
Streaming API - The Force.com Streaming API lets you expose a near real-time stream of data from the Force.com platform. Administrators can create topics, to which applications can subscribe, receiving asynchronous notifications of changes to data in Force.com, via the Bayeux Protocol. Streaming data made simple, secure, and scalable.
Example - You want to display the closed case record in your page in real-time, without refreshing the page you want to display the data in realtime.Refer this link for more details https://developer.salesforce.com/page/Streaming_API