Blocks are a way of wrapping up a piece of code and effectively storing it for later use. A block is commonly used in place of a call back function. Newer APIs in the iPhone SDK use blocks this way. The API will take a "block" of code that it will run on completion. And Blocks are presented in swift as a Closure.
In swift it's little tough syntax to learn closure. but trust me it's very handy way when you start to use it.
It saves you having to create your own threads and maintain the state of each thread, manage locks, setup autorelease pools etc.
Also, when used with the Grand Central Dispatch (GCD) API blocks can be run on queues and entire portions of code can be made to run asynchronously with very little effort, but still keeping the robustness that is required for multithreaded code.