There are many types of energy expended in a household, and while every one can be monetized in some way, the focus is on fuels used to maintain a building's climate and appliances. To be more specific, I mean electricity, natural gas, and propane (maybe wood too) that is used to heat a building or run your TV (screw the rest!).
Be warned that this topic isn't my special-specialty, but I may have done a quarter of my graduate degree on it since every "sustainability" involves energy as much as water -- in fact, it seems like the water portion is the one that's usually forgotten.
Let's start by going over the items you use in the home that requires a fossil fuel directly or indirectly, and electricity. Imagine a nice summer day that isn't too hot or cold -- just right. It's 7 o'clock in the evening, and you're cooking dinner in the kitchen with the TV on. Your stove is either burning gas (natural gas or propane) or using electricity, the ventilation hood above your stove is powered by electricity, as is your television set. Maybe you're a multi-tasker! In the laundry room, you're doing a double load of laundry with both the washer and dryer running; depending on the design, they may be using gas or electricity.
Now, let's make this summer day excruciatingly hot, so your air conditioner is on full blast, which sucks up mucho electricity. Switch it to a winter day and it's likely gas with maybe a space heater or two running. Don't forget to add in the cable box and all other devices on standby, as well as your light bulbs. And your computer is downloading porn and cell phone is charging...
There you have it: the typical electricity and fossil fuel draw in a home found in a developed country.
Like water, we use a lot of resources to make our lives more convenient (enjoyable?). The more electronic toys and conveniences are demanded by each person, or just from growing populations, the more infrastructure and fuel is needed to satisfy the load. That means more pollution in the atmosphere and more expended resources. Also, electricity is a form of energy that, from what I remember, can not be stored easily in very large quantities. Power plants must be able to scale up or down to match the demand at every moment, otherwise whatever is left over usually goes to waste. That is, unless there is a pumped-storage hydroelectricity facility available to store unused energy in the form of potential energy; the basic idea is that you pump the water back up a waterfall to let it fall down again. But again, you need lots of land to store water, so the whole rape and pillaging the environment, scar the face of the earth problem rears its head.
It's your money though and you pay for all that electricity, gas, and water, right? Yep. However, depending on your local utilities arrangement, some of that cost may be subsidized by the government. But let's pretend it's not. Why should you, as an individual, care? Lucky for me, energy conservation is a much bigger story in the media than water, so you've heard the answers already. In summary, it may be due to global warming or an insatiable demand for fuel that requires importing fuels from foreign countries. Otherwise, it may simply come down to money as energy costs are rising to the extent that you can't, or don't want to, pay so much anymore. Whatever your reason is, trying to minimize your energy demand is a "noble" thing to do for the planet and your wallet.
Electricity Demand of Home Appliances and Devices
The electricity usage thing in the home is probably the simplest issue to deal with, so let's get it out of the way. Whatever is plugged in to an outlet uses juice, usually even if it's not on because of standby power requirements (a few watts here or there adds up). Either unplug your devices or get a power bar that can be turned off. Put your computer on standby or shut it down when you're not using it. Most of this comes down to awareness and habits, which may be hard to change, but manageable. To be honest, this is a very "meh" area. Energy efficiency is a big thing and many devices come with built-in power saving features, or each successive iteration is able to do the same (or more) with less. You probably already know about it -- boring. Check out the reference to the DOE to see what the residential electricity breakdown is like; the data is from around 2001.
If you are really curious though, get an electricity usage monitor. It's a device that you plug in between the outlet and your device. The amount of electricity being used is then displayed on the meter's LCD screen in watts (W). You are usually billed by the kilowatt-hour (kWh), which is simply 1000W x 1 hour, or the electricity draw (kW) multiplied by how long it's on (hours). A consumption rate (kWh) multiplied by a unit cost ($/kWh) equals tada! Here's one example: P3 Kill A Watt. Here's another: Belkin Conserve Insight. Not that expensive at about $20-$30. Do some research though as accuracy may vary between makes and models. The best part of these things is that you can find out what the standby draw is. And if you're a nerd, then you probably know about this, but if you don't, then attach it to a computer and see how various activities affect the power draw.
Energy Demand of Homes for Climate Control
I can't remember if this is called "the" biggest energy draw in a typical residential home or not. Regardless, it's one of the big ones. You've heard it before, probably from the government or your utilities: turn your heat down in the winter and your air conditioner "up" in the summer. Bla bla bla, don't leave your windows and doors open, seal those cracks, bla bla bla. Okay, that's the boring and simple part. Because climate control is such a big issue when it comes to energy consumption, there is a branch of engineering that studies the subject in detail known as building science -- they do other things too. Mechanical engineering should also deal with it to some degree, but I'm not a mech engineer, so I don't know.
To celebrate your new found knowledge or appreciation, do go out to start up and rev your F-150!
DOE, 2009. End-Use Consumption of Electricity 2001 U.S.