What the purpose of a singer or vocalist knowing the different breaks in their passagio. Does knowing your passagio points reveal what voice you're in?
Knowing where the breaks between the passagi exist means a singer can match their range to the tessitura of a song, so it can all be sung in a key that works best. It may be that the singer wants the same tone all through, or possibly wants the higher notes using a different voice, at which point, the key for the piece may be a tone or two higher than the first example. Ease of singing and vocal tone.
The locations of the breaks can hint at what your ideal voice type might be. The concept of a "voice type" is somewhat arbitrary but generally seeks to classify singers with other similar sounding singers, either by vocal colour, effective vocal range, technical abilities (read: speed on melismas or trills, etc), or some combination of the three (among other things). One ideally wants to sing in a range that is comfortable and that allows the voice to sound the same throughout the entire vocal range. Knowing where one's passagio(i) is/are helps one technically, but indicating where in the range one needs to "prepare" for the break by bringing in some of the vocal sound from the "other side of the break" to smooth out the transition and eliminate any jumps or bumps in the sound. In addition, greater airflow is often required around the break to assist in this transition. The position of the break is not a hard and fast determinate of your voice type, and only by working with a skilled voice teacher can you ultimately find the voice type best suited to your instrument. The big thing to remember here is that voice type is almost exclusively used to classify singers for opera roles. Outside of the opera world, you just sing whatever you sound good at - and that might mean singing pieces from more than one voice type sometimes - especially if your voice sits "in between" traditional opera voice types.