Metering modes are ways that the camera reads the light in the scene and determines that settings to use. 

They are really only important if you’re shooting in any auto mode, or priority modes.

This includes if you’re shooting in Auto-ISO.

The mode you use will determine how much/what part of the scene to read the light from. This is important to note because if you choose a setting where the camera will only read the exposure of your subject or a very small area of the photo for example, and your dog is black… it will likely determine that the subject is VERY underexposed and set the settings based on that analysis.

Again, this is only important when you’re not shooting in manual exposure. Our goal should still be full manual exposure, so you have the maximum control over the settings.

In any metering mode, there is no difference to the image with ANY metering mode. The only difference I found while conducting some experiments, was the exposure reading, which would tell me if it’s ±0.0 (correctly exposed), +1.0 (one stop over exposed), -1.3 (1.3 stops underexposed) and so on. 

Given that I personally use the histogram as a much more accurate readout of the WHOLE image, the exposure reading isn’t really important for me. If you enjoy using the exposure reading, you may want to take a bit more time to find out what each of the metering modes in your specific camera do.

Each camera will have different modes.

Most of them have some combination of:

• Matrix/Evaluative: generally the default mode, it breaks up the scene into “zones” and evaluates the exposure. Particular importance is based on where the focus point is, and this zone will be given priority. This is a good mode to use if you don’t need something specific or fancy for some reason.
• Centre-weighted. Exposes only based on what’s in the centre of the frame. Could be useful with a not black or white dog, if they’re in the centre of the frame… I guess.
• Spot metering: evaluates the light only based on where your focus point is. This could theoretically be useful if, for example, you’re shooting an agility competition on a day where the clouds are coming and going and the event is faced- paced, so you don’t want to have to constantly keep an eye on your ISO but need it to be auto. Having the metering on spot will mean the subject will be correctly exposed (assuming you focus on them), but could blow out the background elements if they’re especially bright… which is maybe not such a big deal in this particular example.

Other cameras may have other modes, eg., Sony has a “highlights” mode, which reads the entire scene and meters based on the highlights. If I shot in some kind of auto mode, this would mean the settings could be chosen based on not overexposing the highlights.

Check your camera’s manual for any special modes, IF you need them.

But again, if you’re shooting in manual, which I hope you will be, you really don’t need to worry, and leaving it on the default matrix/evaluative is totally fine.