In Vayikra 21:1 it's stated that one should not defile himself for any (dead) nefesh (person).
How can a word like nefesh which seems to be the force that animated the body and gave it it's life, also mean the absence of that same life; death?
The triliteral root (נ-פ-ש) includes the idea of Sabbath rest (see Exod 23:12; 31:17; 2 Sam 16:14). So, depending on the context, the meaning can mean tomb (resting place) or, more commonly, soul/spirit.
R' Samson Raphael Hirsch translates1 "לְנֶפֶשׁ לֹֽא־יִטַּמָּא בְּעַמָּיו" in Leviticus 21:1 simply as "regarding no person among his people may he render himself impure." "נֶפֶשׁ," then, is a generic person, apparently in contradistinction to the family members listed in the next verses, for whom the kohen does "render himself impure."
For a great deal more on what "נֶפֶשׁ" means in this context, according to R' Hirsch, we can turn to his translation of and commentary on the beginning of Parashat Chukat, where the Torah provides the Red Heifer antidote to this form of "impurity."
First, Numbers 19:11:
הַנֹּגֵ֥עַ בְּמֵ֖ת לְכָל־נֶ֣פֶשׁ אָדָ֑ם וְטָמֵ֖א שִׁבְעַ֥ת יָמִֽים׃
He that toucheth the dead body of any human soul becometh unfit for seven days.
R' Hirsch notes that the "dead body" here is of the human soul but is not, in itself, the human soul.
The phrasing gets more interesting in 19:13:
... כָּֽל־הַנֹּגֵ֡עַ בְּמֵ֣ת בְּנֶפֶשׁ֩ הָאָדָ֨ם אֲשֶׁר־יָמ֜וּת
Whosoever cometh into contact with the mortal personality of Man through a dead body which is subject to death ...
If you just look at the Hebrew text, it's a little strange and redundant. It could have just said something like "כָּל הַנֹּגֵעַ בְּמֵת" - "whoever touches a dead body" or "כָּל הַנֹּגֵעַ בְּאָדָם מֵת" - whoever touches a dead human." R' Hirsch explains that the Torah's describing something much bigger here. "הָאָדָם," rather than just plain "אָדָם," is mankind. "הָאָדָם אֲשֶׁר יָמוּת" is "mankind which is mortal." The נֶפֶש of that is "the soul of mortal Man" - the idea that every living human has death hanging over him, which he'll ultimately have no choice but to submit to. Finally, "[all that]כָּל הַנֹּגֵעַ בְּמֵת בְּ" says "one who touches, via a dead body [that great big depressing concept]" (my phrasing, this time).
So, the נֶפֶשׁ, depending on the context, can be the life-force or individuality of a person, or it can be the soul of all humanity, perceived as inexorably doomed. Contact with a dead body can radically alter one's perspective. For more on how such a perspective shift ("impurity") can be a big problem, and how the red heifer process helps, according to R' Hirsch, see the rest of his commentary on the beginning of Chukat, which is very briefly summarized in this answer.
1. This, and all Torah translations and quotations of R' Hirsch presented here, are from the Judaica Press English translation of R' Hirsch's translation and commentary.