Bringing an old but working system up to date — replacing it piece by piece, or rebuilding it — without stopping the business that depends on it daily.
Legacy systems usually still earn money, which is why the big-bang rewrite fails so often: it bets years of budget on a switch-over date that always slips.
We prefer strangling the old system gradually: put a façade in front, move one capability at a time with data kept consistent, and keep both running until the last route is migrated.