A consumer's capacity to afford a house - Expressed in terms of the maximum price the consumer could pay for a house and be approved for the mortgage required to pay that amount.

The way a bank typically calculates affordability is through use of the Debt to Income Ratio.

DTI = Debt/Income

To calculate this the bank relies on the monthly payments that appear on your credit report (car, credit card, loan payments). Your DTI will typically not be calculated using non-Credit reported items suchs as; insurance payments, phone, electric, gas or other utility payents. 

DTI is shown as a percentage- maximum allowable debt to income ratio's are usually around 40% for Back Ratio (housing and other expenses) and 30% for the Front Ration (Just housing expense) 

Bankapedia's Take

 In the glory days of the motgage bubble- affordability meant something very different than it means today. In the midst of the bubble subprime lenders were allowing Back ratio's of as much as 60. Now remember these ratio's dont take into consideration the taxes you have to pay on your income, everything is calculated base off of the gross. It also doesnt factor in utlity expenses, your car insurance, food and other living expenses. With a 60% DTI if you factor in 25% in taxes- you are left with 15% for your utilities, insurance, food, entertainment etc. Imagine if your rate goes up if your in an ARM or your income decreases. Not surprising to see the housing market is in the state it is in. 

Nowadays however lenders have probably overrtightened the screws. With max Back ratio's of 30- sometimes as low as 2Osomething% . Affordability/DTI has in many cases become even more important than ones credit score.