This page will explain how to export a feature layer in ArcGIS Online
Navigate to the desired Feature Layer
Go to the Settings tab and make sure the settings are the same as below:
If you have made any changes press the Save button
Click Export Data
Click Export to Shapefile
See Export to Shapefile window
Type in a Title, one or more Tags, and choose a Folder
Note: The folder is on ArcGIS Online and not on your computer or device
Click Export
See the resulting exported file page
Click Download
The file will download as a zipped file