This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
In security terms, a sandbox is an "area" (which may be more than just memory), that an application can't leave. Furthermore, the application is free to do whatever it likes in the sandbox, as there isn't any damage that it can do that is pernament.
In the case of an Applet, if it were allowed to leave the sandbox, some damage that it can cause is delete files, steal personal information, install viruses, etc. However, since it is confined to the sandbox, it can't do any of that.