For each document, submitting means the action that would normally post it — Mark as open, Publish, Mark as delivered, Issue — which instead sends it for approval when a rule matches (Submitted for approval — it posts automatically once approved). You can also choose Submit for approval from the document's ⋯ menu. A budget is sent with Submit for approval in its editor (see section 13.5).
While a request is pending the document is locked and shows a Pending approval badge; when approved it posts automatically; when rejected it stays a draft, marked Rejected, with the reason on its Approvals tab.
Each list can show just what is waiting: choose Pending approval in the status filter on Invoices, Bills, Expenses or Journals. In the lists a held draft reads Pending approval (or Rejected) instead of Draft.