The Edit Offline action lets you download a file to your computer so you can edit it there. This locks the file in the library to prevent others from editing it simultaneously. It's available for every file.
The Edit Online action lets you edit the file without first saving it offline. It's available only for Microsoft Office 2003 or later files.
The Inline Edit action lets you edit plain text, HTML, or XML files directly in the document library. It's available for these file types, which can all be created with the Create feature in the library.
The Edit in Google Docs action lets you work with files in Google Docs. Like the Edit Offline action, this locks the file in the library while it is being edited. It's available for supported document, presentation, and spreadsheet formats.
You can also edit the properties of a file, or upload content as a new version of an existing file.