In modern armies, Lieutenant General normally ranks immediately below General and above Major General; it is equivalent to the navy rank of Vice Admiral, and in Air Forces with a separate rank structure, it is equivalent to Air Marshal. A Lieutenant General heads up an Army Corps, made up of typically three Army Divisions, and consisting of around 60,000 soldiers.
The term Major General is a shortened version of the previous term Sergeant Major General, which was also subordinate to Lieutenant General. This is why a Lieutenant General outranks a Major General, whereas a Major is senior to a Lieutenant.
In many countries, the rank of Corps General has replaced the earlier rank of Lieutenant General (e.g. France, Italy). (The ranks of corps general and lieutenant colonel general are intended to solve the apparent Lieutenant General / Major General anomaly). However, for convenience, this is often translated into English as Lieutenant General.