The true statement is : Most school and city officers are chosen in this way.
Non partisan means showing no allegiance to any political party ( politically neutral ). When there is a non partisan election, the candidates are elected based on their own merits rather than on their membership in a political party. The merits can be seen as being honest, hard working, trustworthy, friendly and many others. Non partisan elections are usually held for municipal and county offices, school boards and in the process of electing judges.
The main argument behind non partisan election is that people would vote for real people as their representatives rather than blindly voting for a representative of a specific political party.