SharePoint 2013 and SharePoint Online provides a new modern application development model. This new model provides a scalable way to build SharePoint solutions using standards based technologies.
Modern SharePoint apps are built in a way that allows the organization to choose how and where to host the apps. This model also makes it much easier for an organization to move between SharePoint on-premises and SharePoint Online.
To help explain the different development options I have created a SharePoint 2013 development overview slide deck. The intent of this deck is not to teach a person how to do development, but instead to outline the different development models available. With this information an organization can make a well informed decision on how to approach custom development with SharePoint.