First, I'd like to say sorry for the late response—I see your question was posted more than a day ago! Hope I can still be helpful!

There's a few things to establish about what types of income the Spanish crown made from their colonies before I dive in to where that income went. Early conquistadors found the most value out of gold and jewels they stole from Indigenous countries and tribes. Later on, sugar became the most significant moneymaker for Spain. But more than anything else, the key to Spanish colonial wealth was silver, especially in the 1500s and 1600s. Because your question seems mostly to be about what happened with the wealth rather than its origins, and since it was in many ways the most important part of the Spanish empire—and the part I think I'm most qualified to thoroughly discuss—I'll talk about that silver.

In the early 1560s, a massive silver deposit was struck on a plateau of the Andes mountains in modern-day Bolivia. It was the largest silver deposit ever discovered, and a large-scale mining operation the likes of which Dickens would've been shocked about erupted. I won't go into too much detail about that, but suffice it to say that the mining conditions were absolutely terrible and countless "workers" (in reality slave laborers) died there. The city built over the site was named Potosí, and today it's a UNESCO world heritage site.

Here's a few problems: 1. The silver was so concentrated that the Spanish didn't know how to smelt it without burning off more silver (they later "borrowed an indigenous technique and figured it out); 2. The altitude was extremely difficult for Spaniards to bear (which meant that not very many 'honest' Spaniard were willing to go there) and 3. It was an a mountainous area miles away from any other settlements.

Those problems altered where quite a bit of the Spanish silver ended up going. For one thing, the town was relatively lawless. Picture Wild West but in the 1500s. Many Spaniards stole massive sums of silver from the mines, and rival gangs of different Spanish ethnicities (Basque and anti-Basque were the two major factions) that were incredibly wealthy fought each other on the streets. Those gangs made money by refusing to pay taxes, stealing from other gangs, robbing silver shipments, and even owning parts of mines. The Spanish king was lawfully owed one-fifth of all silver produced from the mines at Potosí, but a local tax inspector at the time claimed that the king had been cheated out of 4.5 million pesos. To put that in perspective, that was more than the total output of the mines in one year. Even if that was an overestimate—which some think it may have been—the point is clear: a significant part of Spanish silver was stolen and went into the hands of gangs right from the get-go.

After that, the silver had to be transported via road all the way from the a plateau in the Andes to ports with access to the Caribbean. In Panama, a major section of the road travelled through a long series of swamps, and transports were bogged down regularly in the mud. The same road moves through mountains, so animals meant to pull the loads of silver became tired quickly, not to mention human guards wearing heavy armor. I mention this because along this stretch of road silver was often stolen, and it was relatively commonplace for escaped slaves, pirates, indigenous peoples, or any mixture of said groups to carry out robberies. Not many Spaniards were willing to make that dangerous and long trip, so silver shipments were extremely difficult to get through.

Once the silver had made it to port, there was still a decent chance it'd never get to Spain. That's because despite its value in Spain, it was with even more in China. The Chinese dynasty of the 1500s minted its official currency in silver (and had a host of financial issues) but lacked a solid supply of it, so in order to get any money, they had to literally buy as much silver as they could from other parts of the world. This meant that Spanish traders could exchange silver for what they really wanted—porcelain, silk, spices, and more. Silver was worth more than almost anything else to Chinese merchants, and Chinese trade goods were worth more than almost anything else to Spanish merchants. This meant that, contrary to what the Spanish crown wanted, most of the Spanish silver supply went to Chinese sellers of fine goods. The Philippines was originally established as a Spanish colony for the sole purpose of shipping in silver from the Americas across the Pacific to trade with Chinese merchants. Some estimates go so far to say that 90% of Spanish silver ended up in East Asia.

Even every single one of these obstacles couldn't stop the flow of silver to Spain. To give some sense of the massive scale of the silver operation, in 1549, one single shipment contained 7,771 bars of 99% pure silver, each weighing 60 pounds. One single shipment. All in all, between 1500 and 1700 Spanish silver accounted for 80% of the world's silver output.

So down to answering your question when it comes to Europe. First, we need to understand that pre-colonization Europe was not a particularly wealthy place. In fact, many other parts of the world looked down on Europe as backward, especially China. It's difficult for many to imagine today, but picture the way many Americans and Europeans think about developing countries today, and you'll get a sense of how East Asia (and to a lesser extent the Muslim world) viewed Europe before colonization made it rich.

So all of a sudden, this (relatively) poor nation is getting an absolutely massive injection of wealth directly into its economy. As many nations—and people—with newfound wealth do, Spain overspent. It built massive castles and lavish halls. It maintained a vibrant but expansive court life. It built cathedrals and churches, and helped finance the continuing and expensive Inquisition. Spain embarked on a series of European wars and deals, and the wars of Spanish succession took place during this time, which were extremely expensive.

Perhaps more importantly, Spanish silver was loaned out to other European countries, and later payed to them for loans. The modern system of international finance hadn't really been set up yet, but an early version of it existed. European countries who wanted to pay for wars or domestic projects now had an extremely wealthy neighbor who they could borrow from, and they did. The Hapsburgs spent a decent amount of Spanish silver where they lived. Spain was a creditor for some, and so Spanish silver ended up in other European courts in that way. Later, as Spain continued overspending, it began taking out massive loans to pay for its wars and its decadence, which it was perfectly willing to do because to believed that its "guaranteed" future silver supply would allow it to pay off any loans it took out in the future. Needless to say, that was false, and Spain went bankrupt multiple times. That and regular loan payments led to large sums of formerly Spanish silver being thrown around almost every European court, and Spanish silver helped finance most European wars fought during the colonial era. The entire continent became far more wealthy because of the indirect flow of Spanish silver into their own treasuries through many series of international loans. That newfound wealth helped pay for not only many wars, but also many of Europe's other colonies and projects.

At the same time as its overspending, Spain constantly demanded more and more output from the mines in South America, which only had the effect of overproduction, and as silver flooded the global market its rarity and value decreased. For some time, the Spanish crown raised taxes to the point at which any economic growth was virtually impossible, only because it wanted to sustain it former lavish wars and court life. It later kept them at the same high level regardless of silver supply (like refusing to adjust for inflation). It likewise saw the value of its silver currency plummet, and so economic collapse was not long off.

All in all, after it made it past multiple siphons on the way to Spain, the income from silver mines—the largest source of Spanish colonial wealth—mostly ended up financing the European wars of the 1500s and 1600s, along with giving the continent as a whole quite a bit more relative wealth on the global stage, helping it engage in many of the acts that have led it to be where it is today. Of course, Spanish silver is in no way the only explanation for the world as it is, but it was an influential part of Early Modern Europe.

Sources:

Charles C Mann. 1493: Uncovering the New World Columbus Created. New York: Vintage Books, 2011. Chapters 4 and 8 particularly.

Arzáns de Orsúa y Vela, B. History of the Imperial City of Potosí. Edited by L. Hanke and G. Mendoza. Providence: Brown University Press, 1965.

R. Carande. Carlos V and his bankers. Barcelona: Crítica in Mann.

-edits made for a few typos-