These buttons appear on many of the list screens like Customers, Categories, and Products. They work in the same way regardless of where they occur.
Use the Edit Here button to directly make changes to the information you see on the list, like a product name. Use Edit to go to a complete Edit screen for the product where you can make detailed changes.
In some cases only one of these buttons will be available. For example, on the States screen only Edit Here is available. There is no detailed information about states only what you can see on the list screen, so editing that information in-place is the only option. On the other hand, the Pages screen offers only the Edit button.
Click Edit to go to a screen where you can edit any information about the item.
Click Edit Here to edit just the information you see on the screen.