What is this electrical device in my basement?
That device is a telephone line fuse and surge protector device. The fuses are in line with each of the two telephone line legs. Inside there will be a spark gap to shunt possible lightning on the line to the third center GND wire on the one side. 

These were common in the vintage days when most telephone service was delivered via open wires overhead on poles. These days they are mostly redundant now that most telephone service is delivered underground or may enter the premises through a telephone interface box. These boxes have the surge protections built right into the interface box. 

These days when some folks that still use wired telephone service and also use that service to receive internet service via ADSL or DSL it would be necessary to evaluate the installation to see how the line surge protection is provided. If it is handled by one of these vintage style surge protectors it may be necessary replace devices like these with the more modern style interface box and surge protection to allow the ADSL/DSL signals to pass without attenuation.