An Attach Rate is a economic concept that deals with the number of secondary sales powered by each unit of a primary product sold.
The best example for attach rates - and the area where they are most touted - is with gaming consoles. A PS3 or an Xbox 360 is sold to a consumer as is, it is up to the consumer to purchase gaming software for the product.
For a games publisher, a games console with a higher attach rate would be more desirable than one with a low attach rate. For example, if one console has an attach rate of 6:1, and another has an attach rate of 3:1, then consumers behaviour investing in software for each platform may be considered important.
From the view of the console-maker, the attach rate is also very important, not just for attracting extra third-party titles, but also because the gaming hardware may cost more to produce, box and ship to customers than the customer pays for it. This shortfall is ideally made up by revenue from the sale of software title, as publishers pay a fee for selling games on the platform.
Attach Rates are becoming less important as time goes on in the games industry however, as consoles are becoming more powerful devices capable of catering to all home entertainment needs and not just to boxed games sold at a retailer. There are many more revenue opportunities for console manufacturers now than there was before, and gaming is moving to new models that include digital distribution and even free ad-supported games.
Attach Rate figures can also be very unreliable due to many factors, such as the actions of early adopters and enthusiasts who do not generally represent how the public at large will behave with the same equipment.