What I am aware about the differences between Dual core, Quad core and Octa core is as follows;
Each smartphone needed to develop to cover the trend and advance features to balance competitive business environment and user choice thus they are updating Processor and Core to an advanced one, it is just similar to computer processor types.
Dual core processor have 2 cores and have Hyper threading technology which is far better than normal processor for smartphone.
Quad core processor have 4 cores, it is an advanced feature of Dual core and it has Hyper threading technology and the Turbo boost technology together.
Octa core processor have the same feature as Quad core but it has 8 cores beside Hyper threading technology and the Turbo boost technology in addition to advanced clock speed and media support.
More core means more facility for browsing, speed, data storage, advanced apps, multimedia tasks, video editing, 3D option and HD gaming for a hardcore gamer.