Entire chapters in grammar books have been devoted to this pair of words.
Both words are prepositions.
Some assert that between is used only when referring to two things and that among is used when referring to more than two things. Thus: the spat between my two brothers. Or: the spat among my three brothers.
You should definitely use between when two things are specified: the choice between good and evil; the rivalry between Carolina and Duke.
But when you’re discussing more than two things or the number is unspecified, the choice of between or among depends on your meaning. You restrict the use of between to those situations when the things, entities, or people are specified. You then use among when the things, entities, or people form a collective, a mass.
If you say the meteor landed between the houses, you’re using houses as distinct and specified things. The sentence implies that no house was damaged.
If you say the meteor landed among the houses, you’re using houses as a collective mass. The sentence implies that some houses were damaged.
You can also use among to show inclusion within a group:
He is among the top athletes in the nation.