Compare to a consulate and an embassy, a Consulate General is somewhere between two of them. A Consulate General is very similar to a consulate but provide more range of consular services but has less function than a embassy. It's normally located at a major city.
Services that a consulate general provide include building international relations (such as promoting its country's cultural events and activities) and assist with legal help, criminal assistance and documents request (passport and visa issuing) .
A consul general is the heads of a consulate general and may also be responsible for other smaller consulates in the same host area.