Each person has a different part, and each part could be written for a different instrument.
If two parts were written for violins, the melody (or main tune) was called the first violin part,
and the harmony is called the second violin part.
Two hundred years ago, people did this kind of thing for entertainment.
It was considered fun for people to get together and read and play music. Today we call them "Jam sessions."
The Mozart family would play as a trio.
A trio is music played by three people.