In essence, the biggest impact that Dynamics 365 will have on your organization is by presenting you with more options for your solution.
If you are considering moving more of your business applications to the cloud, this is a great opportunity. As a current Dynamics AX user, you can transition to Dynamics 365 Plan 2 which includes Operations AND Intelligent business applications in the cloud including Sales, Service, Project Service Automation, and PowerApps.
You can take advantage of transition pricing and move your AX solution to the Azure enabled Dynamics 365 solution at the time of your renewal for the next 3 years. If you want to access any of the additional functionality in the meantime, you can leverage the cloud add-on and retain your Dynamics AX on-premise.