Glossary
Vector Image
Short answer
An image defined by mathematical shapes rather than pixels, staying sharp at any size.
A vector image defines shapes as coordinates and curves. That is why it does not degrade when scaled: the same file prints to a favicon and to a shop sign.
Vector is mandatory for logo, icon and typographic work. A pixel logo blurs on signage and loses its detail at favicon size.
Almost every AI tool produces pixels; the one common tool producing vector (SVG) directly is Recraft. A logo idea from any other tool has to be converted to vector before it is usable.