In the United States most banks are insured by the FDIC, for individuals up to $250,000. If I have $200,000 in bank A and bank A fails the FDIC will make sure I get my money back. If I have $400,000 and bank A fails then I will get $250,000 covered by the FDIC, and the remaining $150,000 may or may not come back to me if bank A fails, depending on how the failed bank's money is allocated. Suppose I take my $400,000 and split it between bank A and bank B, $200,000 in each bank. If both bank A and band B fail (unlikely but suppose it did happen) would both deposits be insured by the FDIC, or is the limit per person?
The limit is per account type, per bank, per depositor:
You can easily distribute your millions across multiple banks, or under your spouse's name, or in a different type of account ownership categories (like savings, IRAs, joint accounts, ...), and be covered.