"Respectively" is a typical tricky word, because it is derived from a Latin root, and a similar-looking word is also used in Slovak, but as usual the meanings are different in each language. In Slovak, as far as I can tell, "respektíve" is a sophisticated alternative for "alebo", which I would translate as "or rather", and it is used when people want to correct or re-specify what they have just said.

In English "respectively" is used to link bits of information in order of association with their subjects. First the subjects are presented, then the bits of information are given in the same order as the subjects they are linked with, and then comes the word "respectively" to make it clear. The "long-serving employees" piece contains a typical example. Another example might be that the villa occupants Desperado, Veronika and Saša were voted out in the 4th, 5th and 6th weeks of the Vyvolení "reality show" respectively (you can argue about the number of weeks if you want…).