There are two possible sentences that mean different things:
To say:
The map shows the changes that happened in the area.
is focusing our attention on the changes.
If you break the sentence in two, the parts would read:
The map shows the changes. The changes happened in the area.
To say:
The map shows the changes happened in the area.
omitting that, is focusing our attention on where the changes happened.
To break the sentence in two, the parts would read:
The map shows where the changes happened. They happened in the area.
Thus omitting that gives a completely different emphasis to the sentence.
So you would either include or exclude that depending on what you wanted to say. Grammatically, both are correct.