This from the release notes for 6.4
Paste images - Previously if you had an attachment or image on your clipboard, you had to save it and add it to a JIRA comment or description as an attachment. Now, you can simply copy it directly to JIRA by using your keyboard shortcut or selecting "Copy" from the right-click menu.
For me, this isn't working on any of:
Firefox: 31.6
Chromium: 42.0
IE: 9
Is this down to browser versions?