It might be easier to explain with an example. In this case, I’ll use colors to show you the relationships that are implied between two sets of nouns when you use the word “respectively” at the end of a sentence.
Example: “The peak absorption wavelengths of samples A and B were 710 nm and 600 nm, respectively.”
So in this sentence, we have a set of samples (A and B) and a set of numbers (710 nm and 600 nm). The word “respectively” tells the reader that the samples and numbers that correspond to one another occur in the same order in which they appear. So the first value (710 nm) corresponds to the first sample (A). Likewise, the second value listed in the sentence (600 nm) corresponds the second sample (B).
Let’s do another example.
Example: “The dog and the cat were named Jack and Sam, respectively.”
So what is the dog’s name? And what's the cat’s name?
Since the dog is listed first in the sentence, the word “respectively” lets you know that the dog’s name also corresponds to the first name that’s written (Jack). And since the cat is listed second, its name would be the second name listed in the sentence (Sam).
A note on punctuation: the word "respectively" is put at the end of the sentence or phrase it refers to, and it is set off with a comma (or commas if "respectively" occurs in the middle of the sentence).
Example: The dog and the cat were named Jack and Sam, respectively, and they lived down the street from me.
If you have any doubts about how to use “respectively” in a sentence, I suggest you avoid using it so you don’t unintentionally confuse the reader. It can be a useful writing tool, but it's often not necessary. The sentence can usually be re-written in another way to express the same information.
If you would like to learn more writing tips and tricks, check out my PowerPoint presentation An Introduction to Writing in Science, available in ebook format on the Amazon Kindle app.