Jingoism is a term that can be defined as “excessively enthusiastic patriotism.” You can also say that it is the attitude that one’s own country is always right about everything and that it is better than every other country in essentially every way. Moreover, jingoism is often belligerent, being willing and eager to go to war with other countries.
You can see how this would be connected to American imperialism. If you feel that your country is better than everyone else, you will be more likely to think that your country should rule everyone else. If you are eager to go to war to prove how great your country is, you can easily end up fighting wars that will (like the Spanish-American War) allow you to take an empire. Thus, jingoism helped to fuel American imperialism by making Americans feel superior and belligerent.
The white man’s burden ties into this because it reflected jingoistic ideas. It clearly said that white people were better than everyone else and that they ought to have empires so that they could help all the other people of the world.