I've never heard or read the term 'photometry' before...but multi, spot and average sound like different 'metering' modes.
The camera has a built-in light meter, so that it know what settings to use. You can choose what parts of the scene that the meter uses to make that decision. Spot is probably just the centre area (I doubt it's actually a small 'spot', as that's usually only a feature on high end cameras). The Average is probably just that...an average of the scene...and I'm not sure what 'Multi' is...but it's probably an average of some type.
I'm sure all this is covered in your camera's manual.
In an 'average' scene, you probably won't notice too much of a difference (if any) between the different modes. Where you would notice a difference is when you have something like a back lit subject. For example...lets say you are shooting someone who is standing in a field of snow. If you take an average metering of the scene, all the white snow will make the camera think that it's very bright and your subject will be underexposed and the snow may look grey. The camera doesn't know that the person is your subject...it just sees lots of white and a little bit of darker person.
One solution would be to use the 'spot' metering option and get close to your subject to take a reading. The will make the camera ignore all the stuff outside of the 'spot'...so that your subject will be exposed properly. With most cameras, if you press the button half way...it will keep the settings until you let go or press it fully. In this way, you can get close, take a reading to get the settings then back up and shoot. Some cameras will lock the settings another way, so read your manual.