Synchronous:
In Synchronous process the thread waits for the task to be completed and then moves to the next task Sequentially. All the tasks are completed in a single thread.

Example:
Trigger
Controller Extension
Custom Controller

Asynchronous:
In Asynchronous call, the thread will not wait until it completes its tasks before proceeding to next. In a Asynchronous call, the tasks are run in different threads all together.

Example:
Batch
@future Annotation