These three consonants are Hebrew's word for the verb itself: פֹּעַל literally is the grammatical word for "verb". The root means to act, to operate, to put into effect. From it grow the worker who does the work, the factory where work happens, the action that gets done, and the activist who pushes things into motion. Learn the root and a whole vocabulary of doing falls into place. 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.
Pa'al is the plain action; hif'il makes a machine run; hitpa'el turns the action inward, on the speaker's own feelings (to be moved, impressed). The passive partners nif'al and pu'al are not lexicalized here, so this root lives mainly in three of the seven binyanim.
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.