Explanation/Reference:
1. To add a menu item custom action feature to the app for SharePoint project Right-click the app for SharePoint project, and add a new Menu Item Custom Action item.
2. Select the host web to expose the custom action and choose a list template and custom list as custom action scope to then click on Next button.
3. Enter the menu item text you want to show and page in App where you want to redirect when the user selects the Menu item then click on the Finish button.
Example:

Note: When you are creating an app for SharePoint, custom actions let you interact with the lists and the ribbon in the host web. A custom action deploys to the host web when end users install your app. Custom actions can open a remote webpage and pass information through the query string. There are two types of custom actions available for apps: Ribbon and Menu Item custom actions.
Reference: Custom actions in SharePoint 2013