It was mainly for trade possibilities. It was also for the plunder of the riches of what the Europeans saw as uncivilised countries. The Spanish were ruthless as they stole gold from civilisations in South America. The Spanish, Portuguese, Dutch, British, French and to a smaller extent Germany were sending ships around the world to find business opportunities, generally finding ways to get armies into the countries who soon took over the countries. Asia was seen as good for trade with exotic spices which sold for huge sums back in Europe. Britain's East India Company was so huge it ran its own army which soon dominated India. They exported things like spices and tea from places like India and china and sent back opium causing many Chinese to become addicts. The French and the Dutch had colonies in places like Indonesia and Vietnam. The Portuguese and Spanish concentrated on South America. The British were the masters controlling India and Burma, and plundering Spanish ships transporting stolen gold back from South America. The British people set out to start colonies in North America and also headed South to find good agricultural land in South Africa Australia and New Zealand and pacific islands like Tahiti.
So the Europeans were searching for new lands that they could easily conquer and profit from and in many cases they ruled ruthlessly over their newly conquered countries. Human rights were ignored and if a person protested many European conquerors just locked them up or killed them. Britain and a couple other nations used these new countries to send convicts to get them away from their home countries. Most of the European countries lost control of these conquered countries in the mid 1900s and now they rule themselves.