What is the difference between vector graphics and raster graphics?

I previously understood from the knowledge that there are two different image formats / composition options for creating images; Raster and vector
I want to understand more about them, such as what each definitions feature is, and what usually, generic usage-can be in each case.

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"When You Do Use Other Verses" is a bit broad I think. Need a bit more context (because in digital media, you can often use street images even if the vector will be "the right thing")
I'm looking for an ideal example of an ideal world. I understand that often you have to use the raster image, but I'm just looking for generic use.

Vector graphics are a graphics that the image is presented in a mathematical form. This allows one to zoom in an image with infinite precision. They are ideal for situations that can be used in different resolutions and dimensions.
Raster graphics are a certain dimension, somewhat like a grid pattern with a certain value at each point. These graphics are the default for things in the real world (ie, scanned images, photos, etc.). They can be used only when they are used only when one image is used only once, and will never need to be extended, or if there is no part from photographs or other real-world images.

In general, if you can use vector then this is a good idea. It will be more flexible for scaling, editing will be easy and you do not have to worry about the resolution of the height of the print (vector images are infinite resolution).

Working with two composites is common where you have a photo and other elements.
Perentsotto already keeps it neatly. Still correct in an effort to find the lowest possible definition:

Vector graphics is a collection of geometric elements (circles, squares, triangles, as well as polygons and curves) that you can enlarge any size.

Raster (pixel) graphics are a collection of color dots.

It is not possible to extend without dots to start displaying

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