This is the bare verb to be, the most irregular root in the language and the smallest family here. In the present tense Hebrew drops it entirely (you say "I student", not "I am a student"), so ה־י־ה surfaces mainly in the past, the future, and the infinitive. Push it into the nif'al and "being" tips into becoming: not just existing, but coming to exist. A thin family, but the deepest verb you will ever learn. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
ה־י־ה is defective on every axis: it has no real present tense, and the language has no need to put "to be" through pi'el, hif'il or hitpa'el. The nif'al is the one extra shade it keeps, the shift from being to becoming. The nif'al lemma is given in the first-person past (נִהְיֵיתִי) because that is how pealim cites this irregular verb.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.