1 Technology advancement
As technology advances it allows smartphone manufacturers to create bigger phones. Some manufactures already wanted to create bigger smartphones but were waiting for the proper technology.
2 Smartphones are replacing personal computers
Many people buy smartphones instead of buying a personal computer. Those people expect the phone to be big enough to allow them to do most of the things they used to do on a PC.
3 Customers want the benefits of a Tablet
Samsung said that many customers wanted the benefits of a tablet without buying a tablet.
4 Customers want bigger phones
Smartphone manufactures have realized that customers want larger phones.
5 Larger models succeeded
As many large phones became successful other manufactures started copying them and creating large phones as well. (See Why smartphones are so popular?)
6 Phones are becoming more visual
Phones are shifting away from audio based functions to display based functions. This kind of transition made people realize that they want a larger phone with a larger display.
7 Advancement in battery technology
Early batteries couldn't power a phone with a big screen easily. As technology advanced manufactures were allowed to create phones with bigger screens. (See Why do people buy expensive phones?)