Disposable income is the money you have left over each month after your essential spending.
How it's calculated
This is calculated by taking your total income for the month and taking away all essential spending for the month.
Why lenders want to know about disposable income
Lenders want to see predictable income and that you're responsible with your finances. This is to give them peace of mind that you'll be able to pay back what they lend you.
They look at average spending behaviour over a long period (between 6 months and a year, but it varies by lender). So if you have to spend more than usual for one month, it doesn't matter too much.