The smaller power inverters are portable and very useful in your car as well as at home. If you are going on vacation or even a business trip, the power inverter can be attached to your car battery.
I'm sure you can find many instances when you wish you had the ability to plug something in, but there were no plugs available on the open road. Let's say you're out camping and you use an electric razor. With a power inverter you can take that electric razor with you and feel like you're at home.
Maybe the kids are bored and wish they could listen to a radio or watch television, but they needed to plug in the device to use it. Batteries will eventually run out in these devices. With a power inverter the problem is solved and the kids are happy campers again.