What kind of electrical connection is used for electricity to come to the house from the power generating company?
Power companies generate electricity at the power plant. This electric power needs to be transmitted over large distances to homes. There are two types of electrical currents in use today, DC or Direct Current, and AC or Alternating Current. Historically DC was used first, and popularized by Thomas Edison. However AC proved to be more efficient in delivering electric power to homes without much power loss.
The reason AC is used today to deliver electric power to houses is because it is better at traveling longer distances. Primarily the power lines that you would see over your house are up to 600 volts ac. There the voltage is converted down to 120 volts ac or 220 volts ac (depending on the country in which you live) by a transformer. Now the electricity can be used by home electronic devices and appliances.
AC current works by pushing and pulling electrons about 60 times every second, so that the current doesn't travel through the whole wire; it only pulses. DC is less efficient because the electrons have to travel the entire wire.