Before we get into the term Reference Graphic Card vs Non-Reference Graphic Card, we will first understand the difference between Technology Partners and Manufacturing Partners. Technology Partners are the one who invent technology. Some examples of technology partners are Nvidia and ATI Technologies (AMD) whose focus is to research and develop technologies.
Manufacturing partners are those who purchase these technologies and delivers products. ASUS, Zebronics, XFX are some examples of manufacturing partners. Lets take up an example to understand clear way. Nvidia and ATI develop technologies(graphic cards with technology like PhysX, Eyefinity, TXAA, CUDA etc) and sell to manufacturing partners who manufacture the graphic card itself.
Reference Graphic Card vs Non-Reference Graphic Card
Reference Graphic Cards are those manufactured which strictly comply the specifications of the technology partners. The specifications include the architecture, chipset, GPU, memory, cooling system, design, and even the minor components used in building the graphic cards. GeForce GTX TITAN and GeForce GTX TITAN Z from Nvidia are examples of reference graphic cards. Even these graphic cards are manufactured by manufacturing partners, but with the specifications that comply to technology partners.
Non-Reference Graphic Card are those graphic cards which are modified version of the reference graphic cards. The manufacturing partners make changes (to reference graphic cards) to the design, cooling system, PCB design etc and sell them in the market as non-reference graphic cards. The usual changes in non-reference cards include changes in physical design(size) and cooling system (Fan Sink or Liquid Cooling System) to improve the overall performance of the graphic cards.
Advantages and Disadvantages
It is always the performance which decides whether a graphic card is performing well or not. Sometimes reference graphic cards delivers higher performance and sometimes non-reference graphic deliver higher performance. We can come up with the final answer only by comparing the benchmarks of the graphic cards. Usually reference graphic cards are believed to be stable in terms of hardware, temperature, drivers etc. The reason is that they are developed in such a way that they consume normal power and deliver their optimal performance. But the non-reference graphic cards are overclocked a little higher than normal clock to deliver their best performance which in turn produces more temperature and heat. So the non-reference graphic cards(not all graphic cards) have much better cooling system.
Some graphic cards are available in both reference and non-reference model, while some are available only in reference model.