Competition over the years has driven down the price of fast food (actually, it is ridiculously cheap) to the point where a delivery service makes more financial sense. In large urban centers, where the distances are shorter between restaurants and delivery points, you can more than pay for the costs of delivery, and raise your profit margin at the same time, as people are generally willing to pay more for food they don't have to leave the comforts of home for.
In the past twenty years, we have also seen a large rise in the number of single-parent households in the last twenty years, where one parent is working long hours, and the temptation to buy dinner is greater where the food is the cheapest, such as in these franchises. Also, as businesses and corporations have squeezed expense accounts as a means of coping with the recession, a lot of business travelers who used to eat better on the road, now have to cut corners to meet their per diem allowance.
An increase in consumer income is one of the major reasons that demand for a given good or service can grow. I think that this, possibly along with a decrease in the amount of time available to consumers, is why demand for this service is growing.
As consumers come to have more money and less free time, they will be more willing to pay for this service (which will mean demand will rise). They will be better able to afford the service and it will be of more value to them. If they had a lot of free time, their time would not be so valuable and they would use it to go get the food themselves.
So, as consumers get richer, they are more willing to spend. As they become busier, it is worth more to them to save some time.