An electrostatic generator is a device used for generating static electricity for use in scientific experiments. In fact, that's actually why it was named an Electrostatic Generator. This particular machine is an earlier version of the ones you find in science museums - you know, the things they use to make children's hair stand on end (which teaches them that science can be fun!)
Of course, since there wasn't enough science to fill a science museum in the 18th century, electrostatic generators were of somewhat limited use - until the invention of the Leyden Jar, which could actually store the electricity they created.
Heating a home in the 18th Century posed some problems. You more or less needed a fire - kept in a fireplace - but fireplaces were inefficient, smoky, and had to be built against wall, meaning you were losing heat through the back wall of your house. Not to mention the quantities of wood required to heat a city caused rapid deforestation (yes, people wanted to save the trees even in the 1700s - that's really worked out, hasn't it?)
The stove is essentially a metal fireplace that could be placed in the middle of a room, rather than on the outside. According to Franklin's designs, it could use 1/4 of the wood of a traditional fireplace, but give off twice as much heat. It also had a much smaller chance of giving off a spark that would burn your whole house down, which you've got to admit is an advantage in any heating system.
Franklin was offered a patent on the stove, but he decided not to take it - he wanted people to use his invention free of charge. Which was very philanthropic of him, but others weren't so civic-minded - at least one London merchant pattented a modified version of the stove and made a fortune off of it.
Proof that the world was full of arseholes, even before the internet.