What is the difference between functional and Non-functional requirements

For a software system, there are two kinds of requirements, i.e., Functional and Non-functional Requirements.

Functional Requirements: specify the functionality of the system.

Non-functional Requirements: specify the quality of the system,  is mostly related to the satisfiability of the user.

We use a simplistic Travel Agency Service (TAS) as an example to illustrate the concept. The workflow of the TBS is described as follows. When the request from the user is received, it invokes the other two services based on the request of the user. If the user prefers to Travel by Road, then the Car Booking Service (CBS) is invoked, otherwise if the user prefers to travel by flight, the Flight Booking Service (FBS) is invoked. Subsequently, Hotel Booking Service (HBS) is invoked for booking a hotel for the user, and then the result of the bookings are replied to the user.

In such scenario, the functional requirements of TAS could be:
1) When Travel By Road is chosen, then the CBS will always be invoked.
2) When Travel By Air is chosen, then the FBS will always be invoked.
3) HBS will only be invoked after either CBS or FBS is invoked.
4) HBS and FBS – exactly one of them would be invoked for each request.
etc.

The non-functional requirement of TAS would be
1) TAS responds to users within 3 seconds.
2) The availability of TAS is 99.999%.

etc.

As you can see non-functional is mostly related to the satisfiability of the user; therefore it is often an important clause in service-level agreements (SLAs), which is the contractual basis between service consumers and service providers on the expected Quality of Service (QoS) level.  For example, the SLAs of Amazon.com can be found here.

There are many other non-functional requirement attributes (e.g., Throughput, Latency Time), a more complete list could be found here: http://en.wikipedia.org/wiki/Non-functional_requirement.