Boston baked beans are (usually) navy beans slow cooked in molasses, and often including chunks of pork. It's a dish that dates back to colonial Boston, and is the origin of Boston's "beantown" nickname. Their popularity was probably due to the easy availability of molasses in Boston from the triangular trade between Europe, the Carribean, and the Colonies. (see also the Great Molasses Flood of 1919)

Here's a 1946 recipe from Gourmet Magazine:

2 c Dried navy beans, picked over
- and rinsed
3/4 lb Salt pork
1/2 c Molasses
1/2 ts Dry mustard (english style)
1/4 ts Paprika
1 ts Onion, grated

In a bowl, combine the beans with 4 cups cold water and let them soak overnight. Drain, reserving any remaining liquid. Transfer them to a small heavy kettle, and add fresh water to cover. Simmer, covered, for 60 minutes. Drain in a colander, reserving the cooking liquid and combining it with the soaking liquid.  

To the kettle, add a quarter lb. piece of salt pork and the beans and bury the remaining piece of pork, well scored, in the center of the beans. In a small bowl, stir together the molasses, 1/2 cup of bean liquid, mustard, paprika, and onion. Pour the mixture over the beans and stir in.  

Bake the beans, covered, in the middle of a preheated 300f oven for 5 hours, stirring in some of the bean liquid at hourly intervals as necessary to keep the beans just barely covered. Remove lid and cook uncovered for 1 more hour.