Lt Governor which expands as 'Lieutenant Governor'.
Lieutenant means Deputy or Substitute acting for a superior.

Lt. Governor is used for Governors of Union Territory which has legislative assemblies.

If you want more details Read this explanation:
India is a Quasi Federal Country. Which means States have some powers which can't be taken by Central Government (Except in time of Emergency).
States has Chief Ministers elected by the People of the particular state. Central Government has an agent just to nod head for CM. But he informs all happenings in the state to Central Government. Even though he has some discretionary powers he can do nothing.

But in Case of Union Territories, they are directly administered by Central Government. So there won't be any CM(Yes, Yes, Delhi, Puducherry has one. Wait, Let me deal this first). Central Government appoints an IAS officer for administration. This applies to Union territories like Diu & Daman, Dadra Nagar Haveli, Andaman, Lakshwadeep.

But Puducherry and Delhi have Legislative Assembly which means they have a Leader elected by people. That is Chief Minister. So they are something similar to states. But they are not states. There is no complete power for CM. Many powers reside with Central Government. Eg: Police(Law and Order).
So these 2 Union Territories are unique.
They have CM at the same time strong Central government authority over them.
Who is Central Government? The President.
So, the president controls Union territory. But he can't be there at all time and take care of Union Territory. So he appoints a person responsible.
Under his supervision, Lieutenant Governor is appointed who will overlook all the happenings in Union Territory like Governors of all other states but with more power than other governors of states.