As tectonic processes move the crust around, smooshing it together, bending it, stretching it etc, it also has lots of fluid moving through it. Some are hot, some are cold, some are water based, some are magmatic. They can have wildly different chemistry. As they interact with different rocks at different pressure and temperatures those fluid can dissolve some things. And like putting milk in chocolate cereal - some stuff dissolves into the fluid and others don't.

So while a rock might only contain, say, 0.003% gold, hot fluids with the right temperature, pH and other conditions might be able to dissolve the gold and not much else. That will remove the gold from the rock and put it in the fluid.

As the fluid moves through cracks and other fluid pathways it can cool down or change its solvent properties, and particular minerals will get dumped out of it in highly concentrated volumes.

Lots of ores are not actually found in veins. Massive bodies (like a mound of sulfide having several million tonnes of sulfide minerals in a lens), disseminated ore minerals in huge volumes of rock, and minerals in beds are more common. Some ores are even formed by settling of the ore minerals within mostly-still liquid magma chambers (early-formed minerals act like sediments, in a way). It is only certain types of ores that tend to be found mostly in some sort of vein form.

Mostly, veins are due to the movement (flow) of hot fluids (mostly salty water) through fractures in the rock. The minerals drop out of the fluid and fill the fracture for possible various chemical reasons (change in temp, change in pressure, reaction with the different chemistry of the wall rock). Many massive orebodies, like volcanogenic massive sulfides or sediment-hosted massive sulfides, form when the fractures reach the surface and discharge into a water body (make black smokers, say), so yes, there will be a stockwork of veins beneath the ore but the main ore body is basically a "sedimentary" deposit formed in open water. A good portion of ore mineralization is the result of flowing of hydrothermal fluids, so the underground part will have veins. The vein parts might be pretty poor value though, if the metals only drop out above surface. Lots of quartz and pyrite does not make much of an ore in itself.

Most of the vein-associated ores are ones that have a high dollar value so you don't need a massive amount of the ore to make it an "ore" rather than just an interesting occurrence not worth money to dig it out. Gold is a big one for having a vein-association, and part of this appears to be due to the role of metamorphic dewatering reactions in the formation of certain gold ore types (the fluids never reach surface, and are generated at great depth so the entire mineralization event occurs at substantial depth underground and no massive ores can form). The other part is that chasing veins when they are rich in gold or silver or some metal worth lots of money can be cost effective. No modern mining chases copper or zinc veins like that, unless the entire mountain is filled with lower-grade ore and the huge size makes it worth the effort financially. A dollar per tonne adds up when you deal with millions of tonnes. It does not add up when you are dealing with thousands of tonnes chasing a vein: then you want many dollars per tonne. Remember, t=hat a lot of the cost of mining comes at the start, setting up the very expensive facilities to deal with the ore and make it rich enough to transport cost-effectively.

Sure, early mining did chase veins and very rich zones of mineralization, because the technology for metal recovery was crappy and you needed high grade or the stuff was useless. Mines were created where the ore was clearly visible and very rich. That is often not the case these days. Now, we can recover gold economically even if the stuff is running only a couple-few grams per tonne. The equivalent $$ value of copper though needs a kg per tonne even if you are very efficient at recovery of the metals.

Many mining ventures have re-processed the waste piles from old workings and gotten a lot of that low-grade stuff out, and made money, particularly with respect to high-value metals.

Another side comment is that when a sulfide body deposits on the bottom of the ocean, the water coming from below still keeps coming, and ends up passing through the earlier-deposited sulfides, and lots of fun chemical changes can happen even within the ore body. There will be late veins cutting the earlier massive sulfide, for example.

Mineral ores came from material that was created from a single energetic event and later smushed together. As objects like planets form, lots of different materials get smushed together. This caused a dynamic to develop that spreads the original material out in string-like structures.

It is like when you mix food or stir drinks.

As I understand it, things are deposited essentially flat over an area. Then the same sort of metamorphic processes that create things like marble take over and you end up with veins between layers of rock