Initially, iOS did not have multitasking. Their first attempt was in 2010 (holy crap!). The iPhone just didn't have enough ram and wasn't optimized for it. In 2010, Apple enabled the core apps to multitask, but not 3rd party. I remember jailbreaking my device to bypass that to allow all apps to multitask, but it was buggy. iOS has come a long way folks, with 64bit processing and better memory management.
For further reading, take a look at the Wikipedia article.