For vegetarians what does "balancing complementary proteins" mean?

You first need to understand what complementary proteins are. Complementary proteins are essentially foods people use in place of eating meat so balancing them means that you need to keep track of which ones will give you the neccessary amount that the meat would've given you so that you aren't in a protein defecit 

Think it's rice because in many countries rice is the main food so it can be traditionally served all at once.