There are multiple definitions - click on the translation that matches your context.
residence means:
Substantiv
partial
noun
Since one of the meanings of Aufenthalt has much more of transient connotation (closer to "stay" or "layover"), using "residence" here as a translation requires a context that makes it clear that a longer, legally sanctioned stay was the intended meaning.
the fact that someone lives in a particular place
He claimed that his permanent place of residence was not France.
the house or place where someone lives, especially a large house or a house owned by someone important
More than £700, 000 has been spent on the President's official residence since 2009.
the legal right to live in a country other than the one in which you were born or of which you are a national
The legislation would grant residence to 6,000 immigrants.