Without pi, each content word modifies the preceding phrase individually in succession. pi regroups the following words to modify the preceding phrase as a unit. It is roughly equivalent to hyphenating a phrasaladjective in English.
Using pi followed by one word is proscribed. As there is nothing to regroup, the meaning is unchanged from the same phrase without pi.
If pi is used twice in one phrase, there is no consensus on whether the second pi phrase modifies the first pi phrase (nested), or both modify the head phrase (flat).
pi is often glossed as “of”, in the sense of introducing a postmodifying noun phrase. Using pi for its other senses is proscribed. Note that phrases without pi can be translated using of, as in toki pona, “the language of good”.
While pi can occur before possessive phrases, it does not itself mark the possessive. Compare tomo mi, “my house”, and tomo pi jan Epawan, “Abraham's house”. Both modifiers are possessive; the pi merely groups the two words in the proper name.