The managing broker is responsible for ensuring that a brokerage is compliant with real estate license law. A managing broker may also oversee operations for the brokerage, but that is not always true. Virtually all states require each brokerage to have a managing broker selected. If anything happens to that managing broker, the brokerage must find a replacement.
There can be only one managing broker per brokerage. They are often listed on official real estate documents, brokerage accounts, and transaction records. This way, they can easily be contacted if any compliance issues come up.
The quality of oversight from managing brokers can vary considerably. While managing brokers have many formal responsibilities required by the state, some brokerages are so large, that it is unreasonable for a single managing broker to oversee the activities of thousands of agents.
Broker of record and designated broker are different terms for a managing broker.