Anything that happens under-the-table is taking place secretly, like under-the-table payments that are illegal.
The things on a table are easily seen, but it's not as easy to see what's happening under the table. That can help you remember that under-the-table activities are secret, covert, confidential, and sometimes illegal. If two businesses have an under-the-table agreement, no one else knows about it. If a company pays someone under-the-table, the money is not documented and therefore won't be taxed. Just about everything spies do happens under-the-table.