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“Respective” and “respectively” mean “in the order I mentioned them”. “My mother and sister holidayed in France and Italy respectively” means that my mother went to France and my sister to Italy. Without “respectively”, they would both have gone to both places.
People often use the word just to mean “their own”, as in “they all returned to their respective houses”, but this is wrong. It can usually just be left out: in that last example, without the word “respective” no one would ever assume that they had all returned to random houses.