A razor-blade business model is one that involves initially selling a product for a low price in order to generate revenues from complementary products that it requires to be useful. The term is derived from the classic example: the sale of razors cheap, in order to sell blades at a high margin.
The validity of this example has been questioned, and there are certainly clearer examples. A particularly good example is the sale printers cheap in order to fuel the sales of (very high margin) cartridges. Another is the sale of mobile phones locked to a particular network at loss making prices.
The difference between merely pricing something cheap in order to fuel the sale of complementary good and a razor-blade model is that in the case of a razor-blade model the high margin good is a consumable essential to the (usual) use of the low margin/negative contribution one.
One occasional weakness of razor-blade models is that they are vulnerable to alternative uses of the product sold at a loss: for example the unlocking of mobile phones for use with another network, the modifying of games consoles for use with games not approved by the manufacturer. Another problem can be the availability of alternative sources of the high margin consumable: for example, third party printer cartridges.
Razor-blade models are closely related to those that make use of network effects. Both have been made more common by technology that has been specifically developed to allow manufacturers (and resellers) to control a product after it has been sold.