Why a psu

Solution
Yes, that is what a UPS does, however, unless you spend quite a bit of money, they are really only used to give you enough time to power down your system to prevent damage in case of a power outage. Not really meant to be used as a battery pack for extended use.
The power supply in a PC takes the power from the outlet and distributes it to all your PC components. It converts AC (Alternating current) into a low-voltage DC (Direct current), which is usable by the computer. Without it, your components will not work.

-MystoPigz
 
No. PC components use weird physical connectors and DC electricity. Your wall is 120V AC. To make a weird analogy, your wall is providing diesel but your car runs on gasoline. The PSU would be a magical device which converts diesel to gasoline.

It offers no backup because the PSU doesn't have a battery, it gets the power as-needed from the wall. If you want backup then you need a UPS (uninterruptable power supply) which is a device that has a 120V AC connector and plugs into your wall but then offers up, typically, 4-8 120V AC outlets. A UPS is essentially a fancy power strip with a battery in it.

Your computer's PSU would plug into the UPS rather than the wall. When the power goes out in your house, then the UPS uses its battery to power AC devices like your PSU.

Note that a UPS is good for practically any standard electrical device. You could attach your modem and router to a UPS so that the Internet doesn't go down when the power is out. You could attach a stereo so that you can still play music when the power is out, or a coffee grinder so you can still make coffee. Heck, you could attach a lamp so you can still have lights.
 
ok all great answers, very clear. Is there a system like the psu that actually can be charged and run on its own. Sort of like the power storage units used to plug in a cell phone when the phone battery is low. Could it be the UPS is the closest thing to running the pc like that?
 
Yes, that is what a UPS does, however, unless you spend quite a bit of money, they are really only used to give you enough time to power down your system to prevent damage in case of a power outage. Not really meant to be used as a battery pack for extended use.
 
Solution
Thank you all for the info! I have a better understanding and while both are good investments for their own purpose I have to which would be for me. It sounds like the PCU is the way to go for my usage.
 

One more thing to be clear, it's not either or.
You need a psu. You can add a ups to a pc that has a psu.