How is the word among different than the word between?

In general, use between for two items or people and among for more than two items or people:

The money was to be divided between Romy and Jonathan.
The money was to be divided among Romy, Jonathan, and Brian.

Among suggests a looser relationship than between, and therefore when three or more things are brought into a close, reciprocal relationship, such as they would be with a treaty, between is better than among:

The treaty between Germany, France, and Italy was never ratified.