Well they all had similar motives. They desired economic wealth via extraction, that being the primary form. They would go in and colonize a region in order to extract natural resources from it, including humans in the form of slaves. It also was an ensured market for good produced in the mother country, aka the colonizer.
Another motive for colonization, which was the one used publicly to legitimize their often brutal efforts, was the christianizing\civilizing mission. By presenting christian doctrine, they felt that they would be able to civilize the native population of country x. Of course that does not take into account a pluralistic notion of the way the world works.
There was also the patriotic and political angle. In a time of growing nationalism, people often viewed conquest as a way to show the superiority of their own nation-state. In addition to this, politicians used these overseas struggles as a form of pressure release to distract their populations from problems at home, as well as provide a space where their populations could expand to.