What does connecting my bank actually do?

The bank is the witness. Once connected through Plaid, every posted transaction on that account flows in: deposits land as revenue with the payer worked out where it can be, and card and bank charges land as expenses already sorted into categories. DeskOps also uses the bank to confirm that money a processor says it paid out actually arrived, and to match each payout to a bank line. The connection row shows the window of dates it covers and any gap it knows about, so "the bank says" is never quietly "the bank said, until three weeks ago".