A sandbox is the fence an agent works inside. For Codex, it usually means the workspace folder you opened: it can read and change files there, and needs permission to go beyond it.
On top of the sandbox sits the permission mode. Ask for approval asks you before Codex edits files outside the workspace or uses the internet, and is where OpenAI recommends starting. Approve for me keeps the same fence but sends border crossings to an automatic review. Full access removes the fence. Changing who approves never widens the sandbox itself.