As many people will be aware SAP is changing it's user experience and design philosophy for the better. Fiori along with the
SAPUI5 development platform is the future, not only for mobile but for the overall user interface to SAP.
Or in SAP's words "deliver consumer-grade user experience to our most broadly and frequently used business transactions".
Meaning flowers in Italian, Fiori provides a consistent, responsive user experience (UX) that will allow people to use SAP across various devices. Each app will follow this same philosophy and provide a simple intuitive interface that users will want to use and will help them achieve their goals.
Why is SAP Fiori Different?
There have been many new web development technologies like ITS, BSP and ABAP WDP which provided good options for developing web applications alongside the core SAP GUI reports and transactions. The reason Fiori is different is because SAP have released this as the new version of the SAP GUI and are putting a lot of effort into writing Fiori apps to replicate functionality of the standard SAP system. These apps are also available for free to all SAP customers (the one caveat is that some of them require Hana so you can't use these unless you have Hana, many don't require Hana though). They have also stated that anything new they create will use the SAP Fiori/SAPUI5 route.
SAP UI5 and the future of ABAP
SAP - SAPUI5, Fiori and new UX - Getting Started
Learn SAP UI5 and Fiori in simple way, this course will equip you with knowledge, skills and real life experience.
Check out this and other Fiori courses
More info on SAP Fiori
Getting started with SAP Fiori (inc usful links and demo systems!)
Adding Fiori Apps to your SAP launchpad
Install SAP Web IDE local trial version
Create your first app using the SAP Web IDE
Create an OData Gateway Service using SEGW